A396289 a(n) = n*(12*n+1).

0, 13, 50, 111, 196, 305, 438, 595, 776, 981, 1210, 1463, 1740, 2041, 2366, 2715, 3088, 3485, 3906, 4351, 4820, 5313, 5830, 6371, 6936, 7525, 8138, 8775, 9436, 10121, 10830, 11563, 12320, 13101, 13906, 14735, 15588, 16465, 17366, 18291, 19240, 20213, 21210, 22231, 23276, 24345, 25438, 26555, 27696, 28861, 30050, 31263, 32500, 33761

Offset

0,2

Comments

This is one of a set of 12 sequences that specify the possible moves of a Glinski queen in hexagonal chess (see A396288 for further information).

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

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

Formula

Sum_{n>=1} 1/a(n) = 12 - 3*log(2) - 3*log(3)/2 - sqrt(3)*log(2 + sqrt(3)) - (1 + sqrt(3)/2)*Pi. - Amiram Eldar, May 23 2026

From Elmo R. Oliveira, Jun 01 2026: (Start)

G.f.: x*(13 + 11*x)/(1 - x)^3.

E.g.f.: x*(13 + 12*x)*exp(x).

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

a(n) = A244804(n+1) - 1. - Hugo Pfoertner, Jun 01 2026

Mathematica

A396289[n_] := n*(12*n + 1); Array[A396289, 60, 0] (* Paolo Xausa, May 21 2026 *)

Crossrefs

Cf. A396288, A244804.

Sequence in context: A294520 A189054 A231947 * A322615 A209995 A050410

Adjacent sequences: A396286 A396287 A396288 * A396290 A396291 A396292

Keyword

nonn,easy

Author

N. J. A. Sloane, May 21 2026

Status

approved