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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A193903 is obtained by reversing the rows of the triangle A193902.
LINKS
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

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)