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A193960 Mirror of the triangle A193959. 2
1, 1, 1, 9, 5, 4, 36, 23, 13, 9, 116, 71, 45, 25, 16, 316, 196, 120, 75, 41, 25, 784, 484, 300, 183, 113, 61, 36, 1813, 1121, 692, 428, 260, 159, 85, 49, 3989, 2465, 1524, 940, 580, 351, 213, 113, 64, 8444, 5219, 3225, 1993, 1228, 756, 456, 275, 145, 81 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
A193960 is obtained by reversing the rows of the triangle A193959.
LINKS
FORMULA
Write w(n,k) for the triangle at A193959. The triangle at A193960 is then given by w(n,n-k).
EXAMPLE
First six rows:
1
1.....1
9.....5....4
36....23...13...9
116...71...45...25..16
316...196..120..75..41..25
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
Cf. A193959.
Sequence in context: A259148 A089491 A199792 * A195696 A362000 A197838
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 10 2011
STATUS
approved

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Last modified July 19 18:18 EDT 2024. Contains 374410 sequences. (Running on oeis4.)