A034802 Triangle of Fibonomial coefficients (k=3).

1, 1, 1, 1, 4, 1, 1, 17, 17, 1, 1, 72, 306, 72, 1, 1, 305, 5490, 5490, 305, 1, 1, 1292, 98515, 417240, 98515, 1292, 1, 1, 5473, 1767779, 31716035, 31716035, 1767779, 5473, 1, 1, 23184, 31721508, 2410834608, 10212563270, 2410834608, 31721508, 23184, 1

Offset

0,5

References

A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 88.

Links

G. C. Greubel, Rows n = 0..75 of triangle, flattened

C. Pita, On s-Fibonomials, J. Int. Seq. 14 (2011) # 11.3.7.

Formula

T(n, k) = Product_{j=0..k-1} Fibonacci(3*(n-j))/Product_{j=1..k} Fibonacci(3*j).

Fibonomial coefficients formed from sequence F_4k [ 3 21 144 987 ... ].

Mathematica

F[n_, k_, q_]:= Product[Fibonacci[q*(n-j+1)]/Fibonacci[q*j], {j, k}];
Table[F[n, k, 3], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 13 2019 *)

Prog

(PARI) F(n, k, q) = f=fibonacci; prod(j=1, k, f(q*(n-j+1))/f(q*j)); \\ G. C. Greubel, Nov 13 2019
(Sage)
def F(n, k, q):
    if (n==0 and k==0): return 1
    else: return product(fibonacci(q*(n-j+1))/fibonacci(q*j) for j in (1..k))
[[F(n, k, 3) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 13 2019
(GAP)
F:= function(n, k, q)
    if n=0 and k=0 then return 1;
    else return Product([1..k], j-> Fibonacci(q*(n-j+1))/Fibonacci(q*j));
    fi;
  end;
Flat(List([0..10], n-> List([0..n], k-> F(n, k, 3) ))); # G. C. Greubel, Nov 13 2019

Crossrefs

Cf. A010048.

Sequence in context: A174639 A173814 A176467 * A177262 A203092 A139167

Adjacent sequences: A034799 A034800 A034801 * A034803 A034804 A034805

Keyword

nonn,tabl

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Feb 09 2000

Terms of 8th row corrected by Georg Fischer, Dec 01 2019

Status

approved