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A193903
Mirror of the triangle A193902.
2
1, 1, 2, 3, 6, 4, 7, 14, 12, 8, 15, 30, 28, 24, 16, 31, 62, 60, 56, 48, 32, 63, 126, 124, 120, 112, 96, 64, 127, 254, 252, 248, 240, 224, 192, 128, 255, 510, 508, 504, 496, 480, 448, 384, 256, 511, 1022, 1020, 1016, 1008, 992, 960, 896, 768, 512, 1023, 2046
OFFSET
0,3
COMMENTS
A193903 is obtained by reversing the rows of the triangle A193902.
FORMULA
Write w(n,k) for the triangle at A193902. The triangle at A193903 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1....2
3....6....4
7....14...12...8
15...30...28...24...16
31...62...60...56...48...32
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. A193902.
Sequence in context: A266191 A273338 A099900 * A138728 A291604 A082332
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 08 2011
STATUS
approved