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

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)

Mathematica

Table[10n^2+5n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 16, 51}, 50] (* Harvey P. Dale, Aug 05 2014 *)

Prog

(PARI) a(n)=10*n^2+5*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A080853, A085787.

Sequence in context: A221485 A204723 A204962 * A204716 A192248 A363350

Adjacent sequences: A080857 A080858 A080859 * A080861 A080862 A080863

Keyword

nonn,easy

Author

Paul Barry, Feb 23 2003

Extensions

Definition replaced with the closed form by Bruno Berselli, Jan 16 2013

Status

approved