A035478 Coordination sequence for lattice D*_18 (with edges defined by l_1 norm = 1).

1, 36, 648, 7788, 70416, 511668, 3116952, 16395516, 76117536, 317484356, 1207612584, 4241116044, 13890124080, 42757028820, 124465217976, 344307603996, 908746910784, 2296252865124, 5571657926344, 13017260865708, 29356976611152, 64056799324404, 135523702100952

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

Index entries for linear recurrences with constant coefficients, signature (18, -153, 816, -3060, 8568, -18564, 31824, -43758, 48620, -43758, 31824, -18564, 8568, -3060, 816, -153, 18, -1).

Formula

a(m) = 2^n*binomial((n+2*m)/2-1, n-1) + Sum_{k=0..n} (2^k*binomial(n, k)*binomial(m-1, k-1)), with n=18.

G.f.: (1 +6*x +x^2)*(1 +14*x^2 +x^4)*(1 +12*x +66*x^2 +156*x^3 +111*x^4 -168*x^5 +3740*x^6 -168*x^7 +111*x^8 +156*x^9 +66*x^10 +12*x^11 +x^12) / (1 -x)^18. - Colin Barker, Dec 24 2015

Prog

(PARI) Vec((1 +6*x +x^2)*(1 +14*x^2 +x^4)*(1 +12*x +66*x^2 +156*x^3 +111*x^4 -168*x^5 +3740*x^6 -168*x^7 +111*x^8 +156*x^9 +66*x^10 +12*x^11 +x^12) / (1 -x)^18 + O(x^40)) \\ Colin Barker, Dec 24 2015

Crossrefs

Sequence in context: A287990 A283630 A035713 * A250624 A368062 A231767

Adjacent sequences: A035475 A035476 A035477 * A035479 A035480 A035481

Keyword

nonn,easy

Author

N. J. A. Sloane, J. Serra-Sagrista (jserra(AT)ccd.uab.es)

Status

approved