OFFSET
0,1
COMMENTS
Row sums are: {2, 6, 10, 20, 36, 68, 127, 240, 454, 862, 1640, ...}.
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
T(n, k) = binomial(n, k) + Fibonacci(n) + 1.
G.f.: 1/((-1 + x)*(-1 + y)) + x/((-1 + x + x^2)*(-1 + y)) + 1/(1 - x*(1 + y)). - Stefano Spezia, Nov 22 2019
EXAMPLE
Triangle begins as:
2;
3, 3;
3, 4, 3;
4, 6, 6, 4;
5, 8, 10, 8, 5;
7, 11, 16, 16, 11, 7;
10, 15, 24, 29, 24, 15, 10;
15, 21, 35, 49, 49, 35, 21, 15;
23, 30, 50, 78, 92, 78, 50, 30, 23;
36, 44, 71, 119, 161, 161, 119, 71, 44, 36;
57, 66, 101, 176, 266, 308, 266, 176, 101, 66, 57;
MAPLE
with(combinat); seq(seq(binomial(n, k) +fibonacci(n) +1, k=0..n), n=0..12); # G. C. Greubel, Nov 22 2019
MATHEMATICA
T[n_, k_]:= Binomial[n, k] + Fibonacci[n] + 1; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(PARI) T(n, k) = binomial(n, k)+fibonacci(n)+1; \\ G. C. Greubel, Nov 22 2019
(Magma) [Binomial(n, k)+Fibonacci(n)+1: k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 22 2019
(Sage) [[binomial(n, k)+fibonacci(n)+1 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 22 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, k)+Fibonacci(n) +1))); # G. C. Greubel, Nov 22 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Apr 12 2010
EXTENSIONS
Edited by G. C. Greubel, Nov 22 2019
STATUS
approved