A008921 Coordination sequence for lattice {E_7}*.

1, 56, 938, 7688, 39746, 150248, 455114, 1171928, 2668610, 5521880, 10585514, 19068392, 32622338, 53439752, 84361034, 128991800, 191829890, 278402168, 395411114, 550891208, 754375106, 1017069608, 1352041418, 1774412696, 2301566402, 2953361432, 3752357546, 4724050088, 5897114498

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 (7,-21,35,-35,21,-7,1).

Formula

G.f.: (1+x)*(1 +48*x +519*x^2 +1744*x^3 +1959*x^4 +624*x^5 +x^6)/(1-x)^7.

From G. C. Greubel, Sep 13 2019: (Start)

a(n) = 2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5 for n>0, with a(0)=1.

E.g.f.: -1 + (10 +270*x +2070*x^2 +4200*x^3 +3000*x^4 +804*x^5 +68*x^6) * exp(x)/5. (End)

Maple

seq(`if`(n = 0, 1, 2*(34*n^6-108*n^5+370*n^4-480*n^3+451*n^2-132*n+5)/5 ), n = 0..30); # modified by G. C. Greubel, Sep 13 2019

Mathematica

Table[If[n==0, 1, 2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5], {n, 0, 30}] (* G. C. Greubel, Sep 13 2019 *)

Prog

(PARI) vector(30, n, m=n-1; if(m==0, 1, 2*(5 -132*m +451*m^2 -480*m^3 +370*m^4 -108*m^5 +34*m^6)/5) ) \\ G. C. Greubel, Sep 13 2019
(Magma) [1] cat [2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5: n in [1..30]]; // G. C. Greubel, Sep 13 2019
(Sage) [1]+[2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5 for n in (1..30)] # G. C. Greubel, Sep 13 2019
(GAP) Concatenation([1], List([1..30], n-> 2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5)); # G. C. Greubel, Sep 13 2019

Crossrefs

Sequence in context: A338002 A351410 A219937 * A252181 A251432 A243206

Adjacent sequences: A008918 A008919 A008920 * A008922 A008923 A008924

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms added by G. C. Greubel, Sep 13 2019

Status

approved