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 A193906 Triangular array:  the self-fusion of (p(n,x)), where p(n,x)=sum{F(k+2)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers). 2
 1, 1, 2, 2, 5, 8, 3, 8, 14, 23, 5, 13, 23, 39, 63, 8, 21, 37, 63, 103, 167, 13, 34, 60, 102, 167, 272, 440, 21, 55, 97, 165, 270, 440, 713, 1154, 34, 89, 157, 267, 437, 712, 1154, 1869, 3024, 55, 144, 254, 432, 707, 1152, 1867, 3024, 4894, 7919, 89, 233 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.  The first five rows of P, from the coefficients of p(n,k): 1 1...2 1...2...3 1...2...3...5 1...2...3...5...8 LINKS EXAMPLE First six rows of A193906: 1 1...2 2...5....8 3...8....14...23 5...13...23...39...63 8...21...37...63...103...167 MATHEMATICA z = 12; p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}]; q[n_, x_] := p[n, x] 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}]]  (* A193906 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]]  (* A193907 *) CROSSREFS Cf. A193722, A193907. Sequence in context: A011021 A077232 A193891 * A224791 A210637 A201972 Adjacent sequences:  A193903 A193904 A193905 * A193907 A193908 A193909 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 08 2011 STATUS approved

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Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)