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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A193999 is obtained by reversing the rows of the triangle A094585.
LINKS
FORMULA
Write w(n,k) for the triangle at A094585. The triangle at A094585 is then given by w(n,n-k).
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(n-k+3))))); # Muniru A Asiru, Apr 28 2019
CROSSREFS
Cf. A094585.
Sequence in context: A297878 A234922 A049777 * A210971 A212000 A058401
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 11 2011
EXTENSIONS
Offset 1 from Muniru A Asiru, Apr 29 2019
STATUS
approved

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Last modified May 23 15:19 EDT 2024. Contains 372763 sequences. (Running on oeis4.)