OFFSET
0,8
COMMENTS
The original definition of this sequence did not produce an integer valued triangular sequence. The application of the "round" function was the method chosen to formulate an integer sequence. - G. C. Greubel, Apr 27 2021
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 1, 1;
1, 2, 2, 1;
1, 2, 4, 2, 1;
1, 3, 6, 6, 3, 1;
1, 4, 12, 12, 12, 4, 1;
1, 4, 16, 24, 24, 16, 4, 1;
1, 4, 16, 32, 48, 32, 16, 4, 1;
1, 5, 20, 40, 80, 80, 40, 20, 5, 1;
1, 6, 30, 60, 120, 160, 120, 60, 30, 6, 1;
MATHEMATICA
f[n_]:= f[n]= If[n<3, Fibonacci[n], f[f[n-1]] + f[n-f[n-1]]]; (* f=A004001 *)
c[n_]:= Product[f[j], {j, n}]; (* c=A172452 *)
T[n_, k_]:= Round[c[n]/(c[k]*c[n-k])];
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 27 2021 *)
PROG
(Sage)
@CachedFunction
def b(n): return fibonacci(n) if (n<3) else b(b(n-1)) + b(n-b(n-1)) # b=A004001
def c(n): return product(b(j) for j in (1..n)) # c=A172452
def T(n, k): return round(c(n)/(c(k)*c(n-k)))
[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Apr 27 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Feb 03 2010
EXTENSIONS
Definition changed to give integral terms and edited by G. C. Greubel, Apr 27 2021
STATUS
approved