A035473 Coordination sequence for lattice D*_8 (with edges defined by l_1 norm = 1).

1, 16, 128, 688, 3072, 11472, 36224, 99184, 241664, 535440, 1097344, 2107952, 3834880, 6661200, 11119488, 17932016, 28057600, 42745616, 63597696, 92637616, 132389888, 185967568, 257169792, 350589552, 471732224, 627145360, 824560256, 1073045808, 1383175168

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 (8, -28, 56, -70, 56, -28, 8, -1).

Formula

a(m) = sum(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n)+2^n*binomial((n+2*m)/2-1, n-1), where n=8, a(0)=1.

G.f.: (x^8+8*x^7+28*x^6+56*x^5+326*x^4+56*x^3+28*x^2+8*x+1) / (x-1)^8. [Colin Barker, Nov 19 2012]

Mathematica

CoefficientList[Series[(x^8 + 8 x^7 + 28 x^6 + 56 x^5 + 326 x^4 + 56 x^3 + 28 x^2 + 8 x + 1)/(x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Prog

(Magma) n:=8; [1] cat [&+[2^k*Binomial(n, k)*Binomial(m-1, k-1): k in [0..n]]+2^n*Binomial((n+2*m) div 2-1, n-1): m in [1..30]]; // Bruno Berselli, Oct 21 2013

Crossrefs

Sequence in context: A008535 A008416 A045651 * A014972 A115977 A128692

Adjacent sequences: A035470 A035471 A035472 * A035474 A035475 A035476

Keyword

nonn,easy

Author

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

Extensions

More terms from Vincenzo Librandi, Oct 21 2013

Status

approved