OFFSET
4,3
LINKS
M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, Zeit. f. Kristallographie, 212 (1997), 253-256 and arXiv:cond-mat/9706122.
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
FORMULA
G.f. of n-th row: (Sum_{i=0..n} (binomial(2*n, 2*i) - 2*n*binomial(n-2, i-1))*x^i)/(1-x)^n.
EXAMPLE
1,24,144,456,1056,2040,3504,5544,8256,11736,
1,40,370,1640,4930,11752,24050,44200,75010,119720,
1,60,792,4724,18096,52716,127816,271908,524640,938652,
1,84,1498,11620,55650,195972,559258,1371316,2999682,6003956,
1,112,2592,25424,149568,629808,2100832,5910288,14610560,32641008,
1,144,4194,50832,361602,1801872,6976866,22413456,62407170,155242640,
MATHEMATICA
nmin = 4; nmax = 13; f[x_, n_] := ((1/2)*((-1+Sqrt[x])^(2n)+(1+Sqrt[x])^(2n))*(1-x)^n) / (-1+x)^(2n)-(2n*x*(1+x)^(n-2)) / (1-x)^n; t = Table[ CoefficientList[ Series[ f[x, n], {x, 0, nmax-nmin} ], x], {n, nmin, nmax} ]; Flatten[ Table[ t[[n-k+1, k]], {n, 1, nmax-nmin+1}, {k, 1, n} ] ] (* Jean-François Alcover, Jan 24 2012, after g.f. *)
PROG
(PARI) T(n, k)={polcoeff(sum(i=0, n, (binomial(2*n, 2*i) - 2*n*binomial(n-2, i-1))*x^i)/(1-x)^n + O(x*x^k), k)} \\ Andrew Howroyd, Jul 03 2018
KEYWORD
nonn,tabl
AUTHOR
Ralf Stephan, Feb 21 2005
STATUS
approved