A396288 a(n) = n*(12*n-1).

0, 11, 46, 105, 188, 295, 426, 581, 760, 963, 1190, 1441, 1716, 2015, 2338, 2685, 3056, 3451, 3870, 4313, 4780, 5271, 5786, 6325, 6888, 7475, 8086, 8721, 9380, 10063, 10770, 11501, 12256, 13035, 13838, 14665, 15516, 16391, 17290, 18213, 19160, 20131, 21126, 22145, 23188, 24255, 25346, 26461, 27600, 28763, 29950, 31161, 32396, 33655

Offset

0,2

Comments

This sequence is based on a tiling of the plane by hexagons (often called the hexagonal lattice), with the cells numbered in a counter-clockwise hexagonal spiral starting with index 0 (see A395362).

In Glinski's hexagonal chess, a queen at cell 0 can move in 12 directions, to any cell in the 12 sequences A000567, A049450, A033428, A049451, A045944, A028896; A062783, A396288 (the present sequence), A396289, A063436, A396290, and A396291.

Links

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

Chess variants, Glinski's Hexagonal Chess.

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

Formula

From Stefano Spezia, May 22 2026: (Start)

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

E.g.f.: exp(x)*x*(11 + 12*x). (End)

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

Mathematica

A396288[n_] := n*(12*n - 1); Array[A396288, 60, 0] (* Paolo Xausa, May 21 2026 *)

Crossrefs

Cf. A327131, A395362, A000567, A049450, A033428, A049451, A045944, A028896; A062783, A396288, A396289, A063436, A396290, A396291.

Sequence in context: A116193 A282095 A063158 * A081587 A377663 A223834

Adjacent sequences: A396285 A396286 A396287 * A396289 A396290 A396291

Keyword

nonn,easy

Author

N. J. A. Sloane, May 21 2026

Status

approved