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Search: id:A028552
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| 0, 4, 10, 18, 28, 40, 54, 70, 88, 108, 130, 154, 180, 208, 238, 270, 304, 340, 378, 418, 460, 504, 550, 598, 648, 700, 754, 810, 868, 928, 990, 1054, 1120, 1188, 1258, 1330, 1404, 1480, 1558, 1638, 1720, 1804, 1890, 1978, 2068
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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n(n-3) (n >= 3) is the number of [body] diagonals of an n-gonal prism - Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr).
a(n) = A028387(n)-1. Half of the difference between n(n+1)(n+2)(n+3) and the largest square less than it. Calling this difference "SquareMod": a(n) = (1/2)*SqareMod(n(n+1)(n+2)(n+3)). - Rainer Rosenthal (r.rosenthal(AT)web.de), Sep 04 2004
n != -2 such that x^4 + x^3 - n*x^2 + x + 1 is reducible over the integers. Starting at 10: n such that x^4 + x^3 - n*x^2 + x + 1 is a product of irreducible quadratic factors over the integers. - James Buddenhagen (jbuddenh(AT)gmail.com), Apr 19 2005
If a 3-set Y and a 3-set Z, having two element in common, are subsets of an n-set X then a(n-4) is the number of 3-subests of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Oct 03 2007
Starting with offset 1 = binomial transform of [4, 6, 2, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 09 2009]
a(A002522(n)) = A156798(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2009]
Except for the first term, a(n)=2*n+a(n-1)+2 (with a(1)=4) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
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LINKS
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Milan Janjic, Two Enumerative Functions
P. De Geest, Palindromic Quasipronics of the form n(n+x)
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MAPLE
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a:=n->sum(binomial(n, 1), j=4..n): seq(a(n), n=3..47); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 12 2007
a:=n->sum(sum(3, j=3..n)/3, k=0..n): seq(a(n), n=2..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 30 2007
with (combinat):seq(fibonacci(3, n)+n-3, n=1..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
a:=n->sum(1+sum(1, k=5..n), k=1..n):seq(a(n), n=4...47); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 11 2008
with(finance):seq(add(cashflows([k, k, 2], 0 ), k=1..n), n=0..45); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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MATHEMATICA
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lst={}; Do[AppendTo[lst, n*(n+3)], {n, 0, 6!, 1}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 07 2008]
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CROSSREFS
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Cf. A028387, A062145.
Cf. A002522.
Sequence in context: A009876 A161958 A013921 this_sequence A009877 A009880 A025712
Adjacent sequences: A028549 A028550 A028551 this_sequence A028553 A028554 A028555
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KEYWORD
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nonn,easy,nice,new
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com)
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