A008421 Crystal ball sequence for 10-dimensional cubic lattice.

1, 21, 221, 1561, 8361, 36365, 134245, 433905, 1256465, 3317445, 8097453, 18474633, 39753273, 81270333, 158819253, 298199265, 540279585, 948062325, 1616336765, 2684641785, 4354393801, 6911195501, 10753517061, 16429137361, 24680949041, 36503969061

Offset

0,2

Comments

This is row/column 10 of the Delannoy numbers array, A008288, which is the main entry for these numbers, listing many more properties. - Peter Munn, Jan 05 2023

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

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

Index entries for crystal ball sequences

Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).

Formula

G.f.: (1+x)^10/(1-x)^11.

a(n) = (4*n^10+20*n^9+330*n^8+1200*n^7+7392*n^6+18060*n^5+50270*n^4 +71800*n^3+83754*n^2+50670*n+14175)/14175 - Johannes W. Meijer, Jul 14 2013

Mathematica

CoefficientList[Series[-(z + 1)^10/(z - 1)^11, {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)

Crossrefs

Cf. A001847, A001848, A001849, A008288, A240876.

Sequence in context: A228681 A165223 A152161 * A134585 A165402 A135120

Adjacent sequences: A008418 A008419 A008420 * A008422 A008423 A008424

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved