A035476 Coordination sequence for lattice D*_14 (with edges defined by l_1 norm = 1).

1, 28, 392, 3668, 25872, 147084, 703640, 2936004, 10975776, 37424380, 117743528, 344562484, 943845168, 2433633132, 5936978616, 13769398692, 30495241280, 64756472284, 132333870536, 261119764500, 498982041936

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 (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -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=14, a(0)=1.

G.f.: (x^2 +6*x +1)*(x^12 +8*x^11 +42*x^10 +104*x^9 +335*x^8 -112*x^7 +3340*x^6 -112*x^5 +335*x^4 +104*x^3 +42*x^2 +8*x +1) / (x -1)^14. [Colin Barker, Nov 20 2012]

Mathematica

CoefficientList[Series[(x^2 + 6 x + 1) (x^12 + 8 x^11 + 42 x^10 + 104 x^9 + 335 x^8 - 112 x^7 + 3340 x^6 - 112 x^5 + 335 x^4 + 104 x^3 + 42 x^2 + 8 x + 1)/(x - 1)^14, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Prog

(Magma) n:=14; [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: A283637 A126921 A035709 * A042518 A297179 A269255

Adjacent sequences: A035473 A035474 A035475 * A035477 A035478 A035479

Keyword

nonn,easy

Author

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

Status

approved