A099527 Triangle, read by rows, of trinomial coefficients arranged so that there are n+1 terms in row n by setting T(n,k) equal to the coefficient of z^k in (2 + 3*z + z^2)^(n-[k/2]), for n>=k>=0, where [k/2] is the integer floor of k/2.
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
Offset: 0
Examples
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.
Programs
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PARI
T(n,k)=if(n
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).
Comments