OFFSET
0,5
COMMENTS
Row sums give A167270.
FORMULA
Given Pascal's triangle columns >0, insert 1's as alternate columns.
EXAMPLE
First few rows of the triangle:
1;
1, 1;
1, 2, 1;
1, 3, 1, 1;
1, 4, 1, 3, 1;
1, 5, 1, 6, 1, 1;
1, 6, 1, 10, 1, 4, 1;
1, 7, 1, 15, 1, 10, 1, 1;
1, 8, 1, 21, 1, 20, 1, 5, 1;
1, 9, 1, 28, 1, 35, 1, 15, 1, 1;
1, 10, 1, 36, 1, 56, 1, 35, 1, 6, 1;
1, 11, 1, 45, 1, 84, 1, 70, 1, 21, 1, 1;
1, 12, 1, 55, 1, 120, 1, 126, 1, 56, 1, 7, 1;
1, 13, 1, 66, 1, 165, 1, 210, 1, 126, 1, 28, 1, 1;
1, 14, 1, 78, 1, 220, 1, 330, 1, 252, 1, 84, 1, 8, 1;
1, 15, 1, 91, 1, 286, 1, 495, 1, 462, 1, 210, 1, 36, 1, 1;
1, 16, 1, 105, 1, 364, 1, 715, 1, 792, 1, 462, 1, 120, 1, 9, 1;
...
MATHEMATICA
T[n_, k_] := If[OddQ[k], 1, Binomial[n - k/2, k/2]]; Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Amiram Eldar, Jun 02 2025 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson and Mats Granvik, Oct 31 2009
STATUS
approved
