A194605 Number of ways to place 2 nonattacking kings on an n X n X n X n raumschach board (four-dimensional chessboard).

0, 0, 0, 2080, 27768, 181032, 807040, 2817240, 8271480, 21328048, 49692672, 106717680, 214322680, 406928280, 736614528, 1279735912, 2145244920, 3484996320, 5506324480, 8487206208, 12794341752, 18904506760, 27429548160, 39145417080, 55025652088, 76279746192

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = (n^8 - (3*n-2)^4) / 2 for n>0.

G.f.: 8*x^3*(260+1131*x+750*x^2+335*x^3+75*x^4-30*x^5-x^6)/(1-x)^9. - Bruno Berselli, Aug 31 2011

Crossrefs

Cf. A061995, A166540.

Cf. A194604 for the general d-dimensional case.

Sequence in context: A076581 A183675 A178272 * A233104 A071235 A259414

Adjacent sequences: A194602 A194603 A194604 * A194606 A194607 A194608

Keyword

nonn,easy

Author

Andrew Woods, Aug 30 2011

Status

approved