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A193970 Mirror of the triangle A193969. 2
1, 3, 1, 7, 4, 1, 21, 12, 7, 2, 54, 33, 19, 11, 3, 144, 88, 54, 31, 18, 5, 376, 232, 142, 87, 50, 29, 8, 987, 609, 376, 230, 141, 81, 47, 13, 2583, 1596, 985, 608, 372, 228, 131, 76, 21, 6765, 4180, 2583, 1594, 984, 602, 369, 212, 123, 34, 17710, 10945, 6763 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A193969 is obtained by reversing the rows of the triangle A193970.

LINKS

Table of n, a(n) for n=0..57.

FORMULA

Write w(n,k) for the triangle at A193969.  The triangle at A193970 is then given by w(n,n-k).

EXAMPLE

First six rows:

1

3....1

7....4....1

21...12...7....2

54...33...19...11...3

144..88...54...31...18...5

MATHEMATICA

z = 12;

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

q[n_, x_] := Sum[LucasL[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}]]  (* A193969 *)

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

Flatten[Table[g[n], {n, -1, z}]]  (* A193970 *)

CROSSREFS

Cf. A193969.

Sequence in context: A210038 A319076 A286513 * A274510 A158841 A213576

Adjacent sequences:  A193967 A193968 A193969 * A193971 A193972 A193973

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 10 2011

STATUS

approved

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Last modified February 20 14:03 EST 2020. Contains 332078 sequences. (Running on oeis4.)