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Search: id:A060544
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| A060544 |
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Centered 9-gonal (or nonagonal) numbers. Every third triangular number, starting with a(1)=1. |
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+0
15
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| 1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946, 1081, 1225, 1378, 1540, 1711, 1891, 2080, 2278, 2485, 2701, 2926, 3160, 3403, 3655, 3916, 4186, 4465, 4753, 5050, 5356, 5671, 5995, 6328, 6670, 7021, 7381, 7750, 8128, 8515, 8911, 9316
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Triangular numbers not == 0 (mod 3). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 13 2005
Shallow diagonal of triangular spiral in A051682. - Paul Barry (pbarry(AT)wit.ie), Mar 15 2003
Equals the triangular numbers convolved with [1, 7, 1, 0, 0, 0,...]. [From Gary W. Adamson & Alexander Povolotsky (qntmpkt(AT)yahoo.com), May 29 2009]
Except for the first term, a(n)=9*n+a(n-1), (with a(1)=10) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for two-way infinite sequences
Index entries for sequences related to centered polygonal numbers
Eric Weisstein's World of Mathematics, Marion's Theorem [From Eric W. Weisstein (eric(AT)weisstein.com), Nov 23 2008]
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FORMULA
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a(n)=C(n, 0)+9C(n, 1)+9C(n, 2); binomial transform of (1, 9, 9, 0, 0, 0, .....). a(n)=(9n^2+9n+2)/2. G.f.(1+7x+x^2)/(1-x)^3. - Paul Barry (pbarry(AT)wit.ie), Mar 15 2003
a(n) = C(3n, 3)/n = (3n-1)*(3n-2)/2 = a(n-1)+9(n-1) = A060543(n, 3) = A006566(n)/n = A025035(n)/A025035(n-1) = A027468(n-1)+1 = A000217(3n-2).
G.f.: x(1+7x+x^2)/(1-x)^3. a(1-n)=a(n).
Binomial transform of [1, 9, 9, 0, 0, 0,...]; Narayana transform (A001263) of [1, 9, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2007
a(n)=9*n+a(n-1)-9 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 10 2009]
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EXAMPLE
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For n=2, a(2)=9*2+1-9=10; n=3, a(3)=9*3+10-9=28; n=4, a(4)=9*4+28-9=55 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 10 2009]
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MATHEMATICA
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Transpose[Partition[Accumulate[Range[150]], 3]][[1]] [From Harvey P. Dale (hpd1(AT)nyu.edu), Nov 01 2009]
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PROGRAM
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(PARI) a(n)=(3*n-1)*(3*n-2)/2
(PARI) { for (n=1, 1000, write("b060544.txt", n, " ", (3*n - 1)*(3*n - 2)/2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 06 2009]
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CROSSREFS
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Cf. A027468, A081266.
Cf. A001263.
Sequence in context: A113746 A117464 A081273 this_sequence A088406 A054112 A053790
Adjacent sequences: A060541 A060542 A060543 this_sequence A060545 A060546 A060547
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KEYWORD
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easy,nice,nonn,new
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 02 2001
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EXTENSIONS
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Additional description from Terry Trotter, Apr 06, 2002.
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