A166556 Triangle read by rows, A000012 * A047999

1, 2, 1, 3, 1, 1, 4, 2, 2, 1, 5, 2, 2, 1, 1, 6, 3, 2, 1, 2, 1, 7, 3, 3, 1, 3, 1, 1, 8, 4, 4, 2, 4, 2, 2, 1, 9, 4, 4, 2, 4, 2, 2, 1, 1, 10, 5, 4, 2, 4, 2, 2, 1, 2, 1, 11, 5, 5, 2, 4, 2, 2, 1, 3, 1, 1, 12, 6, 6, 3, 4, 2, 2, 1, 4, 2, 2, 1

Offset

0,2

Links

Table of n, a(n) for n=0..77.

Formula

Triangle read by rows, A000012 * A047999; where A000012 = an infinite lower triangular matrix with all 1's: [1; 1,1; 1,1,1;..]; and A047999 = Sierpinski's gasket.

The operation takes partial sums of Sierpinski's gasket terms, by columns.

Example

First few rows of the triangle =
.1;
.2, 1;
.3, 1, 1;
.4, 2, 2, 1;
.5, 2, 2, 1, 1;
.6, 3, 2, 1, 2, 1;
.7, 3, 3, 1, 3, 1, 1;
.8, 4, 4, 2, 4, 2, 2, 1;
.9, 4, 4, 2, 4, 2, 2, 1, 1;
10, 5, 4, 2, 4, 2, 2, 1, 2, 1;
11, 5, 5, 2, 4, 2, 2, 1, 3, 1, 1;
12, 6, 6, 3, 4, 2, 2, 1, 4, 2, 2, 1;
13, 6, 6, 3, 5, 2, 2, 1, 5, 2, 2, 1, 1;
...

Maple

A166556 := proc(n, k)
    local j;
    add(A047999(j, k), j=k..n) ;
end proc: # R. J. Mathar, Jul 21 2016

Crossrefs

Cf. A047999, A006046 (row sums).

Sequence in context: A138121 A138151 A207378 * A275257 A325027 A306735

Adjacent sequences: A166553 A166554 A166555 * A166557 A166558 A166559

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Oct 17 2009

Status

approved