A035472 Coordination sequence for lattice D*_6 (with edges defined by l_1 norm = 1).

1, 12, 72, 356, 1296, 3708, 8920, 18900, 36384, 65004, 109416, 175428, 270128, 402012, 581112, 819124, 1129536, 1527756, 2031240, 2659620, 3434832, 4381244, 5525784, 6898068, 8530528, 10458540, 12720552, 15358212, 18416496, 21943836

Offset

0,2

Links

Ray Chandler, 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 (6, -15, 20, -15, 6, -1).

Formula

a(m) = Sum_{k=0..n} 2^k*binomial(n, k)*binomial(m-1, k-1) + 2^n*binomial((n+2*m)/2-1, n-1); with n=6.

From Colin Barker, Apr 14 2012: (Start)

a(n)=(4*n*(31+10*n^2+4*n^4))/15 for n>0.

G.f.: (1+6*x+x^2)*(1+14*x^2+x^4)/(1-x)^6. (End)

Prog

(PARI) a(m) = if (m==0, 1, my(n=6); sum(k=0, n, 2^k*binomial(n, k)*binomial(m-1, k-1)) + 2^n*binomial((n+2*m)/2-1, n-1)); \\ Michel Marcus, Mar 19 2021

Crossrefs

Sequence in context: A236967 A227022 A036392 * A036398 A125322 A126480

Adjacent sequences: A035469 A035470 A035471 * A035473 A035474 A035475

Keyword

nonn

Author

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

Status

approved