A213944 Triangle read by rows, with column k defined by partial sums of the finite sequence that contains k three times.

1, 2, 0, 3, 2, 0, 3, 4, 0, 0, 3, 6, 3, 0, 0, 3, 6, 6, 0, 0, 0, 3, 6, 9, 4, 0, 0, 0, 3, 6, 9, 8, 0, 0, 0, 0, 3, 6, 9, 12, 5, 0, 0, 0, 0, 3, 6, 9, 12, 10, 0, 0, 0, 0, 0, 3, 6, 9, 12, 15, 6, 0, 0, 0, 0, 0, 3, 6, 9, 12, 15, 12

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Formula

T(n,k) = 0 if 2k > n+1. T(n,k) = k if 2k=n+1. T(n,k)=2k if 2k=n. T(n,k) = 3k if 2k <= n-1.

Example

First few rows of the triangle are:
1;
2, 0;
3, 2, 0;
3, 4, 0, 0;
3, 6, 3, 0, 0;
3, 6, 6, 0, 0, 0;
3, 6, 9, 4, 0, 0, 0;
3, 6, 9, 8, 0, 0, 0, 0;
3, 6, 9, 12, 5, 0, 0, 0, 0;
3, 6, 9, 12, 10, 0, 0, 0, 0, 0;
3, 6, 9, 12, 15, 6, 0, 0, 0, 0, 0;
3, 6, 9, 12, 15, 12, 0, 0, 0, 0, 0, 0;
...

Mathematica

fs[n_, k_]:=Which[2k>n+1, 0, 2k==n+1, k, 2k==n, 2k, 2k<=n-1, 3k]; Flatten[ Table[ fs[n, k], {n, 15}, {k, n}]] (* Harvey P. Dale, Mar 06 2013 *)

Crossrefs

Cf. A001318 (row sums)

Sequence in context: A120854 A035159 A103489 * A127479 A284124 A187637

Adjacent sequences: A213941 A213942 A213943 * A213945 A213946 A213947

Keyword

nonn,tabl,less,easy

Author

Gary W. Adamson, Jun 25 2012

Status

approved