OFFSET
0,5
COMMENTS
Row sums are: {1, 2, 10, 26, 130, 362, 1810, 5210, 26050, 76490, ...}.
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
T(n, m) = binomial(n, m)*if(floor(n/2) greater than or equal to m then 4^m, otherwise 4^(n-m)).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 8, 1;
1, 12, 12, 1;
1, 16, 96, 16, 1;
1, 20, 160, 160, 20, 1;
1, 24, 240, 1280, 240, 24, 1;
1, 28, 336, 2240, 2240, 336, 28, 1;
1, 32, 448, 3584, 17920, 3584, 448, 32, 1;
1, 36, 576, 5376, 32256, 32256, 5376, 576, 36, 1;
1, 40, 720, 7680, 53760, 258048, 53760, 7680, 720, 40, 1;
MATHEMATICA
Table[Binomial[n, m]*If[Floor[n/2]>=m , 4^m, 4^(n-m)], {n, 0, 10}, {m, 0, n} ]//Flatten
PROG
(PARI) {T(n, k) = binomial(n, k)*if(floor(n/2)>=k, 4^k, 4^(n-k))}; \\ G. C. Greubel, Apr 15 2019
(Magma) [[Floor(n/2) ge k select 4^k*Binomial(n, k) else 4^(n-k)*Binomial(n, k): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Apr 15 2019
(Sage)
def T(n, k):
if floor(n/2)>=k: return 4^k*binomial(n, k)
else: return 4^(n-k)*binomial(n, k)
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Apr 15 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 15 2010
EXTENSIONS
Edited by G. C. Greubel, Apr 15 2019
STATUS
approved