

A193999


Mirror of the triangle A094585.


2



1, 3, 2, 6, 5, 3, 11, 10, 8, 5, 19, 18, 16, 13, 8, 32, 31, 29, 26, 21, 13, 53, 52, 50, 47, 42, 34, 21, 87, 86, 84, 81, 76, 68, 55, 34, 142, 141, 139, 136, 131, 123, 110, 89, 55, 231, 230, 228, 225, 220, 212, 199, 178, 144, 89, 375, 374, 372, 369, 364, 356, 343
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OFFSET

1,2


COMMENTS



LINKS



FORMULA

Write w(n,k) for the triangle at A094585. The triangle at A094585 is then given by w(n,nk).
T(n,k) = Fibonacci(n+3)  Fibonacci(k+2) for n > 0 and 1 <= k <= n.  Rigoberto Florez, Oct 03 2019


EXAMPLE

First six rows:
1;
3, 2;
6, 5, 3;
11, 10, 8, 5;
19, 18, 16, 13, 8;
32, 31, 29, 26, 21, 13;


MATHEMATICA

z = 11;
p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n  k), {k, 0, n}];
q[n_, x_] := x*q[n  1, x] + 1; q[0, n_] := 1;
p1[n_, k_] := Coefficient[p[n, x], x^k];
p1[n_, 0] := p[n, x] /. x > 0;
d[n_, x_] := Sum[p1[n, k]*q[n  1  k, x], {k, 0, n  1}]
h[n_] := CoefficientList[d[n, x], {x}]
TableForm[Table[Reverse[h[n]], {n, 0, z}]]
Flatten[Table[Reverse[h[n]], {n, 1, z}]] (* A094585 *)
TableForm[Table[h[n], {n, 0, z}]]
Flatten[Table[h[n], {n, 1, z}]] (* A193999 *)
(* alternate program *)
Table[Fibonacci[n+3]Fibonacci[k+2], {n, 1, 10}, {k, 1, n}] //TableForm (* Rigoberto Florez, Oct 03 2019 *)


PROG

(GAP) Flat(List([1..11], n>Reversed(List([1..n], k>Fibonacci(n+3)Fibonacci(nk+3))))); # Muniru A Asiru, Apr 28 2019


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



