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A094439 Triangular array T(n,k) = Fibonacci(k+4)*C(n,k), k=0..n, n>=0. 10
3, 3, 5, 3, 10, 8, 3, 15, 24, 13, 3, 20, 48, 52, 21, 3, 25, 80, 130, 105, 34, 3, 30, 120, 260, 315, 204, 55, 3, 35, 168, 455, 735, 714, 385, 89, 3, 40, 224, 728, 1470, 1904, 1540, 712, 144, 3, 45, 288, 1092, 2646, 4284, 4620, 3204, 1296, 233, 3, 50, 360, 1560, 4410, 8568, 11550, 10680, 6480, 2330, 377 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Let F(n) denote the n-th Fibonacci number (A000045). Then n-th row sum of T is F(2n+4) and n-th alternating row sum is -F(n-4).
LINKS
FORMULA
From G. C. Greubel, Oct 30 2019: (Start)
T(n, k) = binomial(n,k)*Fibonacci(k+4).
Sum_{k=0..n} T(n,k) = Fibonacci(2*n+4).
Sum_{k=0..n} (-1)^(k+1) * T(n,k) = Fibonacci(n-4). (End)
EXAMPLE
First few rows:
3;
3, 5;
3, 10, 8;
3, 15, 24, 13;
3, 20, 48, 52, 21;
3, 25, 80, 130, 105, 34;
MAPLE
with(combinat); seq(seq(fibonacci(k+4)*binomial(n, k), k=0..n), n=0..12); # G. C. Greubel, Oct 30 2019
MATHEMATICA
Table[Fibonacci[k+4]*Binomial[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 30 2019 *)
PROG
(PARI) T(n, k) = binomial(n, k)*fibonacci(k+4);
for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Oct 30 2019
(Magma) [Binomial(n, k)*Fibonacci(k+4): k in [0..n], n in [0..12]]; // G. C. Greubel, Oct 30 2019
(Sage) [[binomial(n, k)*fibonacci(k+4) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Oct 30 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, k)* Fibonacci(k+4) ))); # G. C. Greubel, Oct 30 2019
CROSSREFS
Sequence in context: A248955 A071053 A298398 * A122037 A363796 A201454
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, May 03 2004
STATUS
approved

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)