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A193966 Mirror of the triangle A193965. 2
1, 3, 1, 15, 10, 3, 43, 26, 15, 4, 120, 75, 43, 25, 7, 318, 196, 120, 69, 40, 11, 840, 520, 318, 195, 112, 65, 18, 2203, 1361, 840, 514, 315, 181, 105, 29, 5775, 3570, 2203, 1360, 832, 510, 293, 170, 47, 15123, 9346, 5775, 3564, 2200, 1346, 825, 474 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A193966 is obtained by reversing the rows of the triangle A193965.

LINKS

Table of n, a(n) for n=0..52.

FORMULA

Write w(n,k) for the triangle at A193965.  The triangle at A193966 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

3.....1

15....10...3

43....26...15...4

120...75...43...25..7

318...196..120..69..40..11

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

Cf. A193965.

Sequence in context: A181996 A014621 A144006 * A113378 A178657 A257490

Adjacent sequences:  A193963 A193964 A193965 * A193967 A193968 A193969

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)