A193902 Triangular array: the self-fusion of (p(n,x)), where p(n,x)=2x*p(n-1,x)+1, p(0,x)=1.

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.

Links

Table of n, a(n) for n=0..69.

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

Cf. A193722, A193902.

Sequence in context: A127366 A064786 A367286 * A043302 A343964 A345135

Adjacent sequences: A193899 A193900 A193901 * A193903 A193904 A193905

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 08 2011

Status

approved