A008392 Crystal ball sequence for A_8 lattice.

1, 73, 1405, 13237, 79459, 350683, 1240399, 3716695, 9793891, 23301307, 51019255, 104285215, 201186025, 369464785, 650284045, 1102999717, 1811113021, 2889580645, 4493676169, 6829608673, 10167117319, 14854273567, 21334735555, 30167712043, 42050906191, 57846722311

Offset

0,2

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 (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = 143/448*n^8 + 143/112*n^7 + 2431/480*n^6 + 429/40*n^5 + 3355/192*n^4 + 297/16*n^3 + 22079/1680*n^2 + 761/140*n + 1. - T. D. Noe, Apr 29 2007

G.f.: (1 +64*x +784*x^2 +3136*x^3 +4900*x^4 +3136*x^5 +784*x^6 +64*x^7 +x^8)/(1-x)^9. - Colin Barker, Mar 16 2012

Mathematica

LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 73, 1405, 13237, 79459, 350683, 1240399, 3716695, 9793891}, 41] (* G. C. Greubel, May 26 2023 *)

Prog

(Magma) [1 +n*(n+1)*(36528+51788*n+72952*n^2+44473*n^3+27599*n^4 +6435*n^5+2145*n^6)/6720: n in [0..40]]; // G. C. Greubel, May 26 2023
(SageMath) [1+n*(n+1)*(36528+51788*n+72952*n^2+44473*n^3+27599*n^4 +6435*n^5+2145*n^6)/6720 for n in range(41)] # G. C. Greubel, May 26 2023

Crossrefs

Sequence in context: A008400 A090685 A232297 * A221479 A253263 A098676

Adjacent sequences: A008389 A008390 A008391 * A008393 A008394 A008395

Keyword

nonn,easy

Author

N. J. A. Sloane and J. H. Conway

Status

approved