A194713 13 times hexagonal numbers: a(n) = 13*n*(2*n-1).

0, 13, 78, 195, 364, 585, 858, 1183, 1560, 1989, 2470, 3003, 3588, 4225, 4914, 5655, 6448, 7293, 8190, 9139, 10140, 11193, 12298, 13455, 14664, 15925, 17238, 18603, 20020, 21489, 23010, 24583, 26208, 27885, 29614, 31395, 33228, 35113, 37050, 39039, 41080, 43173

Offset: 0

Author

Omar E. Pol, Oct 02 2011

Keywords

• nonn
• easy

Comments

Sequence found by reading the line from 0, in the direction 0, 13, ..., in the square spiral whose vertices are the generalized 15-gonal numbers.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000384, A002939, A094159, A143698, A152745, A154617, A195320.

Programs

Magma

[13*n*(2*n-1): n in [0..50]]; // Vincenzo Librandi, Oct 03 2011

PARI

a(n)=13*n*(2*n-1) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 26*n^2 - 13*n = 13*A000384(n).

a(n) = a(n-1) + 52*n - 39, a(0)=0. - Vincenzo Librandi, Oct 03 2011

From Elmo R. Oliveira, Dec 15 2024: (Start)

G.f.: 13*x*(1 + 3*x)/(1 - x)^3.

E.g.f.: 13*x*(1 + 2*x)*exp(x).

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