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A193902
Triangular array: the self-fusion of (p(n,x)), where p(n,x)=2x*p(n-1,x)+1, p(0,x)=1.
2
1, 2, 1, 4, 6, 3, 8, 12, 14, 7, 16, 24, 28, 30, 15, 32, 48, 56, 60, 62, 31, 64, 96, 112, 120, 124, 126, 63, 128, 192, 224, 240, 248, 252, 254, 127, 256, 384, 448, 480, 496, 504, 508, 510, 255, 512, 768, 896, 960, 992, 1008, 1016, 1020, 1022, 511, 1024, 1536, 1792, 1920, 1984, 2016, 2032, 2040, 2044, 2046, 1023, 2048, 3072, 3584, 3840
OFFSET
0,2
COMMENTS
See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.
EXAMPLE
First six rows of A193902:
1
2....1
4....6....3
8....12...14...7
16...24...28...30...15
32...48...56...60...62...31
MATHEMATICA
z = 12;
p[n_, x_] := x*p[n - 1, x] + 2^n; p[0, x_] := 1;
q[n_, x_] := 2 x*q[n - 1, x] + 1; q[0, x_] := 1;
t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193902 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193903 *)
CROSSREFS
Sequence in context: A127366 A064786 A367286 * A043302 A375305 A343964
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved