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Triangle of rising diagonals of A011973 (with rows displayed as centered text).
0

%I #17 Jul 06 2024 21:27:03

%S 1,1,1,1,1,1,1,1,1,1,3,2,1,1,5,4,1,1,7,6,1,1,1,9,8,6,3,1,1,11,10,15,

%T 10,1,1,13,12,28,21,1,1,1,15,14,45,36,10,4,1,1,17,16,66,55,35,20,1,1,

%U 19,18,91,78,84,56,1,1,1,21,20,120,105,165,120,15,5,1

%N Triangle of rising diagonals of A011973 (with rows displayed as centered text).

%C Row sums are A227300.

%F r(n) = binomial(2n-k-2-3*floor(k/2), floor(k/2)), k = 0..floor((2n-1)/3). - _John Molokach_, Jul 29 2013

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 1, 3, 2;

%e 1, 1, 5, 4;

%e 1, 1, 7, 6, 1;

%e 1, 1, 9, 8, 6, 3;

%e 1, 1, 11, 10, 15, 10;

%e 1, 1, 13, 12, 28, 21, 1;

%t Table[Binomial[2 n - k - 2 - 3 Floor[k/2], Floor[k/2]], {n, 1, 25}, {k, 0, Floor[(2 n - 1)/3]}] (* _John Molokach_, Jul 29 2013 *)

%Y Cf. A011973, A000045, A227300, A005314, A224838.

%K nonn,tabf

%O 1,11

%A _John Molokach_, Jul 27 2013