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A080859
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Generalized polygonal numbers.
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2
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1, 11, 33, 67, 113, 171, 241, 323, 417, 523, 641, 771, 913, 1067, 1233, 1411, 1601, 1803, 2017, 2243, 2481, 2731, 2993, 3267, 3553, 3851, 4161, 4483, 4817, 5163, 5521, 5891, 6273, 6667, 7073, 7491, 7921, 8363, 8817, 9283, 9761, 10251, 10753, 11267
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column T(n,4) of A080853.
Sequence found by reading the line from 1, in the direction 1, 11,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
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FORMULA
| a(n) = C(4, 0)+C(4, 1)n+C(4, 2)n^2 = 6n^2+4n+1 G.f. (C(3, 0)+(C(5, 2)-2)*x+C(3, 2)*x^2)/(1-x)^3 = (1+8x+3x^2)/(1-x)^3
a(n) = A186424(2*n).
a(n)=12*n+a(n-1)-2 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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EXAMPLE
| a(1)=12*1+1-2=11; a(2)=12*2+11-2=33; a(3)=12*3+33-2=67 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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CROSSREFS
| Cf. A001318, A033579, A033581. - Omar E. Pol, Sep 08 2011
Sequence in context: A061833 A132285 A152740 * A063036 A163673 A027025
Adjacent sequences: A080856 A080857 A080858 * A080860 A080861 A080862
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 23 2003
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