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A080860

a(n) = 10*n^2 + 5*n + 1.

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

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OFFSET

0,2

COMMENTS

The old definition of this sequence was "Generalized polygonal numbers".

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

LINKS

Table of n, a(n) for n=0..42.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = C(5,0) + C(5,1)*n + C(5,2)*n^2.

G.f.: (C(4,0) + (C(6,2) - 2)*x + C(4,2)*x^2)/(1-x)^3 = (1 + 13*x + 6*x^2)/(1-x)^3.

a(n) = 20*n + a(n-1) - 5 with n > 0, a(0)=1. - Vincenzo Librandi, Aug 08 2010

From Elmo R. Oliveira, Oct 31 2024: (Start)

E.g.f.: exp(x)*(1 + 15*x + 10*x^2).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

Sum_{n>=0} a(n)/n! = 26*e. - Davide Rotondo, Feb 15 2025

MATHEMATICA