OFFSET
0,1
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
Sum_{k=0..n} T(n,k) = 2^(n+1).
T(n, k) = binomial(n, floor((n+1 - (-1)^(n-k)*(k+1))/2)) + binomial(n, floor(k/2)). - G. C. Greubel, Jan 31 2020
EXAMPLE
Triangle begins:
2;
2, 2;
3, 2, 3;
4, 4, 4, 4;
7, 5, 8, 5, 7;
11, 11, 10, 10, 11, 11;
21, 16, 21, 12, 21, 16, 21;
36, 36, 28, 28, 28, 28, 36, 36;
71, 57, 64, 36, 56, 36, 64, 57, 71; ...
MAPLE
seq(seq( binomial(n, floor((n+1-(-1)^(n-k)*(k+1))/2)) +binomial(n, floor(k/2)), k=0..n), n=0..12); # G. C. Greubel, Jan 31 2020
MATHEMATICA
T[n_, k_]= Binomial[n, Floor[(n+1 -(-1)^(n-k)*(k+1))/2]] + Binomial[n, Floor[k/2]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jan 31 2020 *)
PROG
(PARI) T(n, k) = binomial(n, (n+1 -(-1)^(n-k)*(k+1))\2 ) + binomial(n, k\2); \\ G. C. Greubel, Jan 31 2020
(Magma) [Binomial(n, Floor((n+1 -(-1)^(n-k)*(k+1))/2)) + Binomial(n, Floor(k/2)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 31 2020
(Sage) [[binomial(n, floor((n+1 -(-1)^(n-k)*(k+1))/2)) + binomial(n, floor(k/2)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 31 2020
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, Int((n+1 -(-1)^(n-k)*(k+1))/2)) + Binomial(n, Int(k/2)) ))); # G. C. Greubel, Jan 31 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 25 2007
STATUS
approved