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 A193916 Mirror of the triangle A193915. 2
 1, 1, 2, 2, 4, 4, 4, 8, 12, 16, 7, 14, 24, 40, 48, 12, 24, 44, 80, 128, 160, 20, 40, 76, 144, 256, 416, 512, 33, 66, 128, 248, 464, 832, 1344, 1664, 54, 108, 212, 416, 800, 1504, 2688, 4352, 5376, 88, 176, 348, 688, 1344, 2592, 4864, 8704, 14080, 17408 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A193916 is obtained by reversing the rows of the triangle A193915. LINKS Table of n, a(n) for n=0..54. FORMULA Write w(n,k) for the triangle at A193915. The triangle at A193916 is then given by w(n,n-k). EXAMPLE First six rows: 1 1....2 2....4....4 4....8....12...16 7....14...24...40...48 12...24...44...80...128...160 MATHEMATICA z = 12; p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}]; 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}]] (* A193908 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]] (* A193909 *) CROSSREFS Cf. A193915, A193909. Sequence in context: A306060 A317238 A260038 * A304347 A316218 A305642 Adjacent sequences: A193913 A193914 A193915 * A193917 A193918 A193919 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 09 2011 STATUS approved

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Last modified November 29 07:03 EST 2023. Contains 367429 sequences. (Running on oeis4.)