A008398 Crystal ball sequence for E_7 lattice.

1, 127, 3025, 28911, 162417, 652431, 2086241, 5659295, 13561889, 29504095, 59400241, 112234255, 201127185, 344628207, 568250433, 906272831, 1403829569, 2119308095, 3127077265, 4520566831, 6415719601, 8954837583, 12310843425, 16691978463, 22346958689, 29570609951

Offset

0,2

Links

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

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).

Index entries for crystal ball sequences

Formula

a(n) = 1 + (2/105)*n*(222*n^6 + 756*n^5 + 1260*n^4 + 1470*n^3 + 1708*n^2 + 1029*n + 170).

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(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). - Harvey P. Dale, Jul 18 2012

Maple

seq(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, n=0..30);

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
(Magma) [1 +(2/105)*n*(222*n^6 +756*n^5 +1260*n^4 +1470*n^3 +1708*n^2 +1029*n +170): n in [0..30]]; // G. C. Greubel, May 29 2023
(SageMath)
def A008398(n): return 1 +2*n*(222*n^6 +756*n^5 +1260*n^4 +1470*n^3 +1708*n^2 +1029*n +170)//105
[A008398(n) for n in range(31)] # G. C. Greubel, May 29 2023

Crossrefs

Sequence in context: A321552 A321546 A345458 * 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