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A008398 Crystal ball sequence for E_7 lattice. 1
1, 127, 3025, 28911, 162417, 652431, 2086241, 5659295, 13561889, 29504095, 59400241, 112234255, 201127185, 344628207, 568250433, 906272831, 1403829569, 2119308095, 3127077265, 4520566831 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for crystal ball sequences

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 linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

FORMULA

a(n) = 148/35*n^7+72/5*n^6+24*n^5+28*n^4+488/15*n^3+98/5*n^2+68/21*n+1 (see MAPLE lines).

G.f.: (1+119*x+2037*x^2+8211*x^3+8787*x^4+2037*x^5+119*x^6+x^7)/(1-x)^8. [Colin Barker, Mar 16 2012]

a(0)=1, a(1)=127, a(2)=3025, a(3)=28911, a(4)=162417, a(5)=652431, a(6)=2086241, a(7)=5659295, 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)  From Harvey P. Dale, Jul 18 2012

MAPLE

148/35*n^7+72/5*n^6+24*n^5+28*n^4+488/15*n^3+98/5*n^2+68/21*n+1;

MATHEMATICA

Table[148/35n^7+72/5n^6+24n^5+28n^4+488/15n^3+98/5n^2+68/21n+1, {n, 0, 20}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 127, 3025, 28911, 162417, 652431, 2086241, 5659295}, 20] (* Harvey P. Dale, Jul 18 2012 *)

PROG

(PARI) a(n)=(444*n^7 + 1512*n^6 + 2520*n^5 + 2940*n^4 + 3416*n^3 + 2058*n^2 + 340*n + 105)/105 \\ Charles R Greathouse IV, Feb 10 2017

CROSSREFS

Sequence in context: A258808 A321552 A321546 * A144969 A114535 A215611

Adjacent sequences:  A008395 A008396 A008397 * A008399 A008400 A008401

KEYWORD

nonn,easy,nice

AUTHOR

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

STATUS

approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)