OFFSET
0,5
COMMENTS
Row sums are: 1, 2, 9, 16, 26, 40, 73, 114, 204, 336, 552, ...
LINKS
G. C. Greubel, Rows n = 0..100 of the triangle, flattened
FORMULA
T(n, k, q) = Sum_{j=0..10} q^j * floor(A174093(n, k)/2^j), for q = 1.
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 7, 1;
1, 7, 7, 1;
1, 7, 10, 7, 1;
1, 8, 11, 11, 8, 1;
1, 10, 18, 15, 18, 10, 1;
1, 11, 26, 19, 19, 26, 11, 1;
1, 15, 39, 38, 18, 38, 39, 15, 1;
1, 16, 53, 67, 31, 31, 67, 53, 16, 1;
1, 18, 70, 109, 67, 22, 67, 109, 70, 18, 1;
MATHEMATICA
A174093[n_, k_]:= If[n<2, 1, Binomial[n-k+1, k] + Binomial[k+1, n-k]];
T[n_, k_, q_]:= Sum[q^j*Floor[A174093[n, k]/2^j], {j, 0, 10}];
Table[T[n, k, 1], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Feb 10 2021 *)
PROG
(Sage)
def A174093(n, k): return 1 if n<2 else binomial(n-k+1, k) + binomial(k+1, n-k)
def T(n, k, q): return sum( q^j*(A174093(n, k)//2^j) for j in (0..10) )
flatten([[T(n, k, 1) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 10 2021
(Magma)
A174093:= func< n, k | n lt 2 select 1 else Binomial(n-k+1, k) + Binomial(k+1, n-k) >;
T:= func< n, k, q | (&+[ q^j*Floor(A174093(n, k)/2^j): j in [0..10]]) >;
[T(n, k, 1): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 10 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 07 2010
EXTENSIONS
Edited by G. C. Greubel, Feb 10 2021
STATUS
approved