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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
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 (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.

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

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)