OFFSET
0,5
COMMENTS
Row sums = A131405: (1, 2, 7, 16, 37, 82, 179, ...).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1274
FORMULA
T(n,k) = 4*binomial(n, k) + 1 - 2*binomial(floor((n + k)/2), k) - 2*binomial(n-floor((k+1)/2), floor(k/2)). - Andrew Howroyd, Aug 09 2018
EXAMPLE
First few rows of the triangle are:
1;
1, 1;
1, 5, 1;
1, 7, 7, 1;
1, 11, 13, 11, 1;
1, 13, 27, 27, 13, 1;
1, 17, 39, 65, 39, 17, 1;
...
PROG
(PARI) T(n, k) = if(k <= n, 4*binomial(n, k) + 1 - 2*binomial((n + k)\2, k) - 2*binomial(n-(k+1)\2, k\2), 0) \\ Andrew Howroyd, Aug 09 2018
(Magma) /* As triangle */ [[4*Binomial(n, k) + 1 - 2*Binomial(Floor(n + k) div 2, k) - 2*Binomial(n-Floor((k+1)/2), Floor(k/2)): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Aug 10 2018
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Jul 07 2007
EXTENSIONS
Terms a(55) and beyond from Andrew Howroyd, Aug 09 2018
STATUS
approved