A396291 - OEIS

%I #17 May 23 2026 05:59:12

%S 0,7,38,93,172,275,402,553,728,927,1150,1397,1668,1963,2282,2625,2992,

%T 3383,3798,4237,4700,5187,5698,6233,6792,7375,7982,8613,9268,9947,

%U 10650,11377,12128,12903,13702,14525,15372,16243,17138,18057,19000,19967,20958,21973,23012,24075,25162,26273,27408,28567,29750,30957,32188,33443

%N a(n) = n*(12*n-5).

%C 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).

%H Paolo Xausa, <a href="/A396291/b396291.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F From _Stefano Spezia_, May 22 2026: (Start)

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

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

%F 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

%t A396291[n_] := n*(12*n - 5); Array[A396291, 60, 0] (* _Paolo Xausa_, May 21 2026 *)

%Y Cf. A396288.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, May 21 2026