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A080860
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Generalized polygonal numbers.
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1
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1, 16, 51, 106, 181, 276, 391, 526, 681, 856, 1051, 1266, 1501, 1756, 2031, 2326, 2641, 2976, 3331, 3706, 4101, 4516, 4951, 5406, 5881, 6376, 6891, 7426, 7981, 8556, 9151, 9766, 10401, 11056, 11731, 12426, 13141, 13876, 14631, 15406, 16201, 17016, 17851
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column T(n,5) of A080853.
Sequence found by reading the line from 1, in the direction 1, 16,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Sep 10 2011
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FORMULA
| a(n) = C(5, 0)+C(5, 1)n+C(5, 2)n^2 = 10n^2+5n+1 G.f. (C(4, 0)+(C(6, 2)-2)*x+C(4, 2)*x^2)/(1-x)^3 = (1+13x+6x^2)/(1-x)^3
a(n)=20*n+a(n-1)-5 (with a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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EXAMPLE
| a(1)=20*1+1-5=16; a(2)=20*2+16-5=51; a(3)=20*3+51-5=106 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 08 2010]
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CROSSREFS
| Sequence in context: A121864 A204723 A204962 * A204716 A192248 A044118
Adjacent sequences: A080857 A080858 A080859 * A080861 A080862 A080863
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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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