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 A193965 Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{L(k+1)*x^(n-k) : 0<=k<=n}, where L=A000032 (Lucas numbers). 2

%I #6 Mar 30 2012 18:57:39

%S 1,1,3,3,10,15,4,15,26,43,7,25,43,75,120,11,40,69,120,196,318,18,65,

%T 112,195,318,520,840,29,105,181,315,514,840,1361,2203,47,170,293,510,

%U 832,1360,2203,3570,5775,76,275,474,825,1346,2200,3564,5775,9346

%N Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{L(k+1)*x^(n-k) : 0<=k<=n}, where L=A000032 (Lucas numbers).

%C See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

%e First six rows:

%e 1

%e 1...3

%e 3...10...15

%e 4...15...26...43

%e 7...25...43...75...120

%e 11..40...69...120..196..318

%t z = 12;

%t p[n_, x_] := Sum[LucasL[k + 1]*x^(n - k), {k, 0, n}];

%t q[n_, x_] := p[n, x];

%t t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;

%t w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

%t g[n_] := CoefficientList[w[n, x], {x}]

%t TableForm[Table[Reverse[g[n]], {n, -1, z}]]

%t Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193965 *)

%t TableForm[Table[g[n], {n, -1, z}]]

%t Flatten[Table[g[n], {n, -1, z}]] (* A193966 *)

%Y Cf. A193722, A193966.

%K nonn,tabl

%O 0,3

%A _Clark Kimberling_, Aug 10 2011

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Last modified August 3 05:44 EDT 2024. Contains 374875 sequences. (Running on oeis4.)