A154218 Modified Fibonomial matrix.

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 9, 12, 9, 1, 1, 20, 45, 45, 20, 1, 1, 48, 160, 300, 160, 48, 1, 1, 117, 624, 1820, 1820, 624, 117, 1, 1, 294, 2457, 12012, 18200, 12012, 2457, 294, 1, 1, 748, 9996, 78897, 198016, 198016, 78897, 9996, 748, 1

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for the first 51 rows

Formula

T(n,k) = A010048(n,k)*(1 + F(k)*F(n-k)).

Example

Triangle begins
1,
1, 1,
1, 2, 1,
1, 4, 4, 1,
1, 9, 12, 9, 1,
1, 20, 45, 45, 20, 1.

Maple

A154218 := proc(n, k)
    A010048(n, k)*(1+combinat[fibonacci](k)*combinat[fibonacci](n-k)) ;
end proc:
seq(seq(A154218(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Feb 05 2015

Mathematica

f[n_, k_] := Product[Fibonacci[n - j + 1]/Fibonacci[j], {j, k}]; Table[f[n, i]*(1 + Fibonacci[i]*Fibonacci[n - i]), {n, 0, 10}, {i, 0, n}] (* G. C. Greubel, Sep 04 2016 *)

Crossrefs

Row sums are A154219.

Sequence in context: A202549 A155971 A176480 * A326326 A307139 A078121

Adjacent sequences: A154215 A154216 A154217 * A154219 A154220 A154221

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 05 2009

Status

approved