A035475 Coordination sequence for lattice D*_12 (with edges defined by l_1 norm = 1).

1, 24, 288, 2312, 14016, 68664, 288096, 1071912, 3600768, 11036504, 31125408, 81412680, 199013440, 457923960, 998269920, 2073758312, 4126016256, 7897561752, 14598964768, 26150436744, 45523755456, 77217221304, 127904389728

Offset

0,2

Links

Vincenzo Librandi, 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 (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Formula

a(m)=add(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n)+2^n*binomial((n+2*m)/2-1, n-1); with n=12.

G.f.: (x^4+4*x^3+22*x^2+4*x+1)*(x^8+8*x^7+12*x^6-8*x^5+230*x^4-8*x^3+12*x^2+8*x+1) / (x-1)^12. - Colin Barker, Nov 20 2012

Mathematica

CoefficientList[Series[(x^4 + 4 x^3 + 22 x^2 + 4 x + 1) (x^8 + 8 x^7 + 12 x^6 - 8 x^5 + 230 x^4 - 8 x^3 + 12 x^2 + 8 x + 1)/(x - 1)^12, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Crossrefs

Sequence in context: A297082 A282154 A035707 * A288458 A042110 A282993

Adjacent sequences: A035472 A035473 A035474 * A035476 A035477 A035478

Keyword

nonn,easy

Author

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

Status

approved