A193956 - OEIS

A193956

Mirror of the triangle A193955.

1, 4, 1, 13, 5, 1, 45, 23, 9, 2, 120, 71, 36, 14, 3, 300, 196, 116, 59, 23, 5, 692, 484, 316, 187, 95, 37, 8, 1524, 1121, 784, 512, 303, 154, 60, 13, 3225, 2465, 1813, 1268, 828, 490, 249, 97, 21, 6625, 5219, 3989, 2934, 2052, 1340, 793, 403, 157, 34, 13280

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OFFSET

0,2

COMMENTS

A193956 is obtained by reversing the rows of the triangle A193955.

LINKS

Table of n, a(n) for n=0..55.

FORMULA

Write w(n,k) for the triangle at A193955. The triangle at A193955 is then given by w(n,n-k).

EXAMPLE

First six rows:

4.....1

13....5....1

45....23...9....2

120...71...36...14..3

300...192..116..59..23..5

MATHEMATICA

z = 12;

p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];

q[n_, x_] := Sum[((k + 1)^2)*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}]] (* A193955 *)

TableForm[Table[g[n], {n, -1, z}]]

Flatten[Table[g[n], {n, -1, z}]] (* A193956 *)

CROSSREFS

Cf. A193955.

Sequence in context: A357216 A055252 A318945 * A193843 A116414 A215502

Adjacent sequences: A193953 A193954 A193955 * A193957 A193958 A193959

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved