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A193905
Mirror of the triangle A193904.
2
1, 1, 2, 3, 6, 8, 7, 14, 24, 32, 15, 30, 56, 96, 128, 31, 62, 120, 224, 384, 512, 63, 126, 248, 480, 896, 1536, 2048, 127, 254, 504, 992, 1920, 3584, 6144, 8192, 255, 510, 1016, 2016, 3968, 7680, 14336, 24576, 32768, 511, 1022, 2040, 4064, 8064, 15872
OFFSET
0,3
COMMENTS
A193905 is obtained by reversing the rows of the triangle A193904.
FORMULA
Write w(n,k) for the triangle at A193904. The triangle at A193905 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....2
3....6....8
7....14...24....32
15...30...56....96....128
31...62...120...224...384...512
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}]] (* A193904 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193905 *)
CROSSREFS
Cf. A193904.
Sequence in context: A211603 A221956 A249549 * A127293 A355296 A138343
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved