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A094444 Triangular array T(n,k) = Fibonacci(n+4-k)*C(n,k), k=0..n, n>=0.

%I A094444 #8 Sep 08 2022 08:45:13
%S A094444 3,5,3,8,10,3,13,24,15,3,21,52,48,20,3,34,105,130,80,25,3,55,204,315,
%T A094444 260,120,30,3,89,385,714,735,455,168,35,3,144,712,1540,1904,1470,728,
%U A094444 224,40,3,233,1296,3204,4620,4284,2646,1092,288,45,3,377,2330,6480,10680,11550,8568,4410,1560,360,50,3
%N A094444 Triangular array T(n,k) = Fibonacci(n+4-k)*C(n,k), k=0..n, n>=0.
%C A094444 Row sums are Fibonacci numbers.
%C A094444 Row sums with alternating signs are Fibonacci numbers or their negatives.
%H A094444 G. C. Greubel, <a href="/A094444/b094444.txt">Rows n = 0..100 of triangle, flattened</a>
%F A094444 From _G. C. Greubel_, Oct 30 2019: (Start)
%F A094444 T(n,k) = binomial(n,k)*Fibonacci(n-k+4).
%F A094444 Sum_{k=0..n} T(n,k) = Fibonacci(2*n+4).
%F A094444 Sum_{k=0..n} (-1)^(k+1) * T(n,k) = (-1)^n * Fibonacci(n-4). (End)
%e A094444 First few rows:
%e A094444    3;
%e A094444    5,   3;
%e A094444    8,  10,   3;
%e A094444   13,  24,  15,  3;
%e A094444   21,  52,  48, 20,  3;
%e A094444   34, 105, 130, 80, 25, 3;
%p A094444 with(combinat); seq(seq(fibonacci(n-k+4)*binomial(n,k), k=0..n), n=0..12); # _G. C. Greubel_, Oct 30 2019
%t A094444 Table[Fibonacci[n-k+4]*Binomial[n,k], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Oct 30 2019 *)
%o A094444 (PARI) T(n,k) = binomial(n,k)*fibonacci(n-k+4);
%o A094444 for(n=0,12, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Oct 30 2019
%o A094444 (Magma) [Binomial(n,k)*Fibonacci(n-k+4): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Oct 30 2019
%o A094444 (Sage) [[binomial(n,k)*fibonacci(n-k+4) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Oct 30 2019
%o A094444 (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n,k)*Fibonacci(n-k+4) ))); # _G. C. Greubel_, Oct 30 2019
%Y A094444 Cf. A000045, A094435, A094436, A094437, A094438, A094439, A094440, A094441, A094442, A094443.
%K A094444 nonn,tabl
%O A094444 0,1
%A A094444 _Clark Kimberling_, May 03 2004