A225800 Triangle of rising diagonals of A011973 (with rows displayed as centered text).

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

Offset

1,11

Comments

Row sums are A227300

Links

Table of n, a(n) for n=1..76.

Formula

r(n) = binomial[2n-k-2-3floor(k/2),floor(k/2)); {k, 0,...,floor((2n-1)/3)}. - John Molokach, Jul 29 2013

Example

Triangle begins:
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, 10;
1, 1, 13, 12, 28, 21, 1;

Mathematica

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 *)

Crossrefs

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

Sequence in context: A046225 A269233 A123396 * A176669 A327615 A058280

Adjacent sequences: A225797 A225798 A225799 * A225801 A225802 A225803

Keyword

nonn,tabf

Author

John Molokach, Jul 27 2013

Status

approved