A396291 a(n) = n*(12*n-5).

0, 7, 38, 93, 172, 275, 402, 553, 728, 927, 1150, 1397, 1668, 1963, 2282, 2625, 2992, 3383, 3798, 4237, 4700, 5187, 5698, 6233, 6792, 7375, 7982, 8613, 9268, 9947, 10650, 11377, 12128, 12903, 13702, 14525, 15372, 16243, 17138, 18057, 19000, 19967, 20958, 21973, 23012, 24075, 25162, 26273, 27408, 28567, 29750, 30957, 32188, 33443

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

From Stefano Spezia, May 22 2026: (Start)

G.f.: x*(7 + 17*x)/(1 - x)^3.

E.g.f.: exp(x)*x*(7 + 12*x). (End)

Sum_{n>=1} 1/a(n) = (6*log(2) + 3*log(3) - 2*sqrt(3)*log(2 + sqrt(3)) + (sqrt(3) - 2)*Pi) / 10. - Amiram Eldar, May 23 2026

Mathematica

A396291[n_] := n*(12*n - 5); Array[A396291, 60, 0] (* Paolo Xausa, May 21 2026 *)

Crossrefs

Cf. A396288.

Sequence in context: A346278 A165495 A369355 * A034858 A249354 A381310

Adjacent sequences: A396288 A396289 A396290 * A396292 A396293 A396294

Keyword

nonn,easy

Author

N. J. A. Sloane, May 21 2026

Status

approved