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

Author

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

Keywords

• nonn
• easy

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).

Programs

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

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 *)

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

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