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A193959 Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{((k+1)^2)*x^(n-k) : 0<=k<=n} and q(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) . 2
1, 1, 4, 5, 9, 9, 13, 23, 36, 16, 25, 45, 71, 116, 25, 41, 75, 120, 196, 316, 36, 61, 113, 183, 300, 484, 784, 49, 85, 159, 260, 428, 692, 1121, 1813, 64, 113, 213, 351, 580, 940, 1524, 2465, 3989, 81, 145, 275, 456, 756, 1228, 1993, 3225, 5219, 8444 (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....1
4....5....9
9....13...23...36
16...25...45...71....116
25...41...75...120...196...316
MATHEMATICA
z = 12;
p[n_, x_] := Sum[((k + 1)^2)*x^(n - k), {k, 0, n}]
q[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
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}]] (* A193959 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]] (* A193960 *)
CROSSREFS
Sequence in context: A218505 A128891 A172180 * A093667 A243591 A189012
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved

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Last modified July 21 21:50 EDT 2024. Contains 374475 sequences. (Running on oeis4.)