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A193960 Mirror of the triangle A193959. 3
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

Table of n, a(n) for n=0..54.

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 A197838 A155534

Adjacent sequences:  A193957 A193958 A193959 * A193961 A193962 A193963

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified July 17 03:18 EDT 2019. Contains 325092 sequences. (Running on oeis4.)