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Search: id:A080855
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| A080855 |
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Generalized polygonal numbers. |
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+0
6
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| 1, 4, 16, 37, 67, 106, 154, 211, 277, 352, 436, 529, 631, 742, 862, 991, 1129, 1276, 1432, 1597, 1771, 1954, 2146, 2347, 2557, 2776, 3004, 3241, 3487, 3742, 4006, 4279, 4561, 4852, 5152, 5461, 5779, 6106, 6442, 6787, 7141, 7504, 7876, 8257, 8647, 9046
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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row T(3,n) of A080853
a(n) is also the least weight of self-conjugate partitions having n different parts such that each part is congruent to 2 modulo 3. The first such self-conjugate partitions, corresponding to a(n)=1,2,3,4, are 2+2, 5+5+2+2+2, 8+8+5+5+5+2+2+2, 11+11+8+8+8+5+5+5+2+2+2. [From Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
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REFERENCES
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A. O. Munagi, Pairing conjugate partitions by residue classes, Discrete Math., 308 (2008), 2492--2501.
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FORMULA
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a(n)=(9n^2-3n+2)/2 G.f.: (1+x+7x^2)/(1-x)^3
Equals binomial transform of [1, 3, 9, 0, 0, 0,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 30 2008
a(n)=9*n+a(n-1)-15 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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EXAMPLE
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For n=2, a(2)=9*2+1-15=4; n=3, a(3)=9*3+4-15=16; n=4, a(4)=9*4+16-15=37 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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MATHEMATICA
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s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 500, 9}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]
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CROSSREFS
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Cf. A027468, A038764 [From Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
Sequence in context: A030158 A054246 A080709 this_sequence A103770 A121318 A152133
Adjacent sequences: A080852 A080853 A080854 this_sequence A080856 A080857 A080858
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KEYWORD
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easy,nonn,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 23 2003
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