A035721 Coordination sequence for 26-dimensional cubic lattice.

1, 52, 1352, 23452, 305552, 3191812, 27866072, 209284972, 1381251872, 8143343572, 43450388072, 212064570172, 955155127472, 4000059761572, 15676069223672, 57810425102092, 201600442152512, 667669374615412

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

Index entries for linear recurrences with constant coefficients, signature (26, -325, 2600, -14950, 65780, -230230, 657800, -1562275, 3124550, -5311735, 7726160, -9657700, 10400600, -9657700, 7726160, -5311735, 3124550, -1562275, 657800, -230230, 65780, -14950, 2600, -325, 26, -1).

Formula

G.f.: ((1+x)/(1-x))^26.

For n >= 1, a(n) = (4/3698160658676859375)*k*(4*k^24 +5200*k^22 +2696980*k^20 +729500200*k^18 +113058092290*k^16 +10403235809200*k^14 +571033266394960*k^12 +18358560436559200*k^10 +331670354541689020*k^8 +3134604254001277200*k^6 +13742418871540936746*k^4 +22474514386734286500*k^2 +8373940585251924375). - Robert Israel, Oct 21 2016

n*a(n) = 52*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 21 2018

Mathematica

CoefficientList[Series[((1+x)/(1-x))^26, {x, 0, 20}], x] (* Harvey P. Dale, Mar 19 2017 *)

Crossrefs

Sequence in context: A130000 A160153 A017768 * A035798 A017715 A112008

Adjacent sequences: A035718 A035719 A035720 * A035722 A035723 A035724

Keyword

nonn,easy

Author

Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

Extensions

Recomputed by N. J. A. Sloane, Nov 25 1998

Status

approved