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A008392
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Crystal ball sequence for A_8 lattice.
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4
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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
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OFFSET
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0,2
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LINKS
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J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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