OFFSET
0,2
COMMENTS
Row sums form A099528. In general if T(n,k) = coefficient of z^k in (a + b*z + c*z^2)^(n-[k/2]), then the resulting number triangle will have the o.g.f.: ((1-a*x-c*x^2*y^2) + b*x*y)/((1-a*x-c*x^2*y^2)^2 - x*(b*x*y)^2).
FORMULA
G.f.: (1-x*(2-3*y)-x^2*y^2)/(1-4*x+x^2*(4-2*y^2)-5*x^3*y^2+x^4*y^4).
EXAMPLE
Rows begin:
[1],
[2,3],
[4,12,1],
[8,36,13,6],
[16,96,66,63,1],
[32,240,248,360,33,9],
[64,576,800,1560,321,180,1],
[128,1344,2352,5760,1970,1683,62,12],
[256,3072,6496,19152,9420,10836,985,390,1],
[512,6912,17152,59136,38472,55692,8989,5418,100,15],...
and can be derived from the coefficients of (2+3*z+z^2)^n:
[1],
[2,3,1],
[4,12,13,6,1],
[8,36,66,63,33,9,1],
[16,96,248,360,321,180,62,12,1],
[32,240,800,1560,1970,1683,985,390,100,15,1],...
by shifting each column k down by [k/2] rows.
PROG
(PARI) T(n, k)=if(n<k || k<0, 0, polcoeff((2+3*z+z^2+z*O(z^k))^(n-k\2), k, z))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Oct 20 2004
STATUS
approved