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).

1, 1, 3, 3, 10, 15, 4, 15, 26, 43, 7, 25, 43, 75, 120, 11, 40, 69, 120, 196, 318, 18, 65, 112, 195, 318, 520, 840, 29, 105, 181, 315, 514, 840, 1361, 2203, 47, 170, 293, 510, 832, 1360, 2203, 3570, 5775, 76, 275, 474, 825, 1346, 2200, 3564, 5775, 9346

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..53.

Example

First six rows:
1
1...3
3...10...15
4...15...26...43
7...25...43...75...120
11..40...69...120..196..318

Mathematica

z = 12;
p[n_, x_] := Sum[LucasL[k + 1]*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}]]  (* A193965 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]  (* A193966 *)

Crossrefs

Cf. A193722, A193966.

Sequence in context: A236170 A129885 A277963 * A301279 A330288 A262923

Adjacent sequences: A193962 A193963 A193964 * A193966 A193967 A193968

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 10 2011

Status

approved