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A154218
Modified Fibonomial matrix.
2
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
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 * A373744 A326326 A307139
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jan 05 2009
STATUS
approved