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 A008360 Crystal ball sequence for D_7 lattice. 4

%I

%S 1,85,1583,13203,68853,264825,824083,2195399,5195081,11199037,

%T 22392919,42088091,75111165,128274849,210937851,335661583,518971409,

%U 782230181,1152631807,1664322595,2359658117,3290603337,4520283747

%N Crystal ball sequence for D_7 lattice.

%H Alois P. Heinz, <a href="/A008360/b008360.txt">Table of n, a(n) for n = 0..10000</a> [Replaces an earlier corrupted file]

%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).

%H <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).

%F a(n) = (2*n+1)*(242*n^6+726*n^5+1856*n^4+2502*n^3+2207*n^2+1077*n+315)/315.

%F From _Harvey P. Dale_, Sep 15 2011: (Start)

%F 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).

%F 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)

%p 1/315 * (2*n+1)*(242*n^6+726*n^5+1856*n^4+2502*n^3+2207*n^2+1077*n+315);

%t 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 *)

%o (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

%o (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

%o (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

%o (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

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_ and _J. H. Conway_

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Last modified August 20 03:33 EDT 2019. Contains 326139 sequences. (Running on oeis4.)