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A193968 Mirror of the triangle A193967. 2
1, 1, 1, 7, 4, 3, 19, 12, 7, 4, 54, 33, 21, 11, 7, 142, 88, 54, 33, 18, 11, 376, 232, 144, 87, 54, 29, 18, 985, 609, 376, 232, 141, 87, 47, 29, 2583, 1596, 987, 608, 376, 228, 141, 76, 47, 6763, 4180, 2583, 1596, 984, 608, 369, 228, 123, 76, 17710, 10945 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A193967 is obtained by reversing the rows of the triangle A193968.

LINKS

Table of n, a(n) for n=0..56.

FORMULA

Write w(n,k) for the triangle at A193967.  The triangle at A193968 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

1....1

7....4....3

19...12...7...4

54...33...21..11..7

142..88...54..33..18..11

MATHEMATICA

z = 12;

p[n_, x_] := Sum[LucasL[k + 1]*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}]]  (* A193967 *)

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

Flatten[Table[g[n], {n, -1, z}]]  (* A193968 *)

CROSSREFS

Cf. A193968.

Sequence in context: A065477 A272526 A100041 * A153840 A198351 A245074

Adjacent sequences:  A193965 A193966 A193967 * A193969 A193970 A193971

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified September 16 18:26 EDT 2021. Contains 347473 sequences. (Running on oeis4.)