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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
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
Sequence in context: A236170 A129885 A277963 * A301279 A330288 A262923
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved

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Last modified July 19 02:27 EDT 2024. Contains 374388 sequences. (Running on oeis4.)