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A008360 Crystal ball sequence for D_7 lattice. 4
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)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000 [Replaces an earlier corrupted file]

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 (8, -28, 56, -70, 56, -28, 8, -1).

FORMULA

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

From Harvey P. Dale, Sep 15 2011: (Start)

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)

MAPLE

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A189439 A166917 A206377 * A212474 A020310 A163692

Adjacent sequences:  A008357 A008358 A008359 * A008361 A008362 A008363

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified July 21 22:02 EDT 2019. Contains 325210 sequences. (Running on oeis4.)