OFFSET
2,4
COMMENTS
Row sums = A120739: (1, 2, 7, 14, 30, 60, 127, 254, ...).
LINKS
Reinhard Zumkeller, Rows n = 2..125 of triangle, flattened
FORMULA
T(n, m) = floor(binomial(n, m)/2). - Roger L. Bagula, Mar 07 2010
EXAMPLE
First few rows of the triangle:
1;
1, 1;
2, 3, 2;
2, 5, 5, 2;
3, 7, 10, 7, 3;
3, 10, 17, 17, 10, 3;
4, 14, 28, 35, 28, 14, 4;
4, 18, 42, 63, 63, 42, 18, 4;
5, 22, 60, 105, 126, 105, 60, 22, 5;
5, 27, 82, 165, 231, 231, 165, 82, 27, 5;
6, 33, 110, 247, 396, 462, 396, 247, 110, 33, 6;
...
MAPLE
seq(seq(floor(binomial(n, m)/2), m=1..n-1), n=2..12); # Muniru A Asiru, Apr 14 2019
MATHEMATICA
T[n_, m_] = Floor[Binomial[n, m]/2]; Table[T[n, m], {n, 2, 12}, {m, 1, n-1}]//Flatten (* Roger L. Bagula, Mar 07 2010*)
PROG
(Haskell) Following Bagula's formula
a166454 n k = a166454_tabl !! (n-2) !! (k-1)
a166454_row n = a166454_tabl !! (n-2)
a166454_tabl = map (map (flip div 2) . init . tail) $ drop 2 a007318_tabl
-- Reinhard Zumkeller, Mar 04 2015
(GAP) Flat(List([2..12], n->List([1..n-1], m->Int(Binomial(n, m)/2)))); # Muniru A Asiru, Apr 14 2019
(PARI) {T(n, k) = binomial(n, k)\2 };
for(n=2, 12, for(k=1, n-1, print1(T(n, k), ", "))) \\ G. C. Greubel, Apr 16 2019
(Magma) [[Floor(Binomial(n, k)/2): k in [1..n-1]]: n in [2..12]]; // G. C. Greubel, Apr 16 2019
(Sage) [[floor(binomial(n, k)/2) for k in (1..n-1)] for n in (2..12)] # G. C. Greubel, Apr 16 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Oct 14 2009
STATUS
approved