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A008360
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Crystal ball sequence for D_7 lattice.
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4
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1, 85, 1583, 13203, 68853, 264825, 824083, 2195399, 5195081, 11199037, 22392919, 42088091, 75111165, 128274849, 210937851, 335661583, 518971409, 782230181, 1152631807, 1664322595, 2359658117, 3290603337, 4520283747
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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) = (2*n+1)*(242*n^6+726*n^5+1856*n^4+2502*n^3+2207*n^2+1077*n+315)/315.
a(0)=1, a(1)=85, a(2)=1583, a(3)=13203, a(4)=68853, a(5)=264825, a(6)=824083, a(7)=2195399, a(n)=8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8).
G.f.: (x^7+77*x^6+931*x^5+2863*x^4+2863*x^3+931*x^2+77*x+1)/(x-1)^8. (End)
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MAPLE
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1/315 * (2*n+1)*(242*n^6+726*n^5+1856*n^4+2502*n^3+2207*n^2+1077*n+315);
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MATHEMATICA
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Table[1/315 (2n+1)(242n^6+726n^5+1856n^4+2502n^3+2207n^2+1077n+315), {n, 0, 20}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 85, 1583, 13203, 68853, 264825, 824083, 2195399}, 20] (* Harvey P. Dale, Sep 15 2011 *)
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PROG
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(Magma) [1/315*(2*n+1)*(242*n^6+726*n^5+1856*n^4+2502*n^3+2207*n^2+1077*n+315): n in [0..30]]; // Vincenzo Librandi, Sep 16 2011
(PARI) a(n)=(2*n+1)*(242*n^6+726*n^5+1856*n^4+2502*n^3+2207*n^2+1077*n+315)/315 \\ Charles R Greathouse IV, Sep 16 2011
(PARI) Vec((x^7+77*x^6+931*x^5+2863*x^4+2863*x^3+931*x^2+77*x+1)/(x-1)^8 + O(x^100)) \\ Altug Alkan, Mar 18 2016
(JavaScript) function A008360(n){ var N=bigInt(n); return String(N.times(2).next().times(N.times(242).plus(726).times(N).plus(1856).times(N).plus(2502).times(N).plus(2207).times(n).plus(1077).times(N).plus(315)).over(315))} // Precede by <script src="http://peterolson.github.com/BigInteger.js/BigInteger.min.js" ></script> - M. F. Hasler, Mar 17 2016
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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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