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A168258 Triangle read by rows, A097806 * A111967 as infinite lower triangular matrices. 3
1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 3, 3, 3, 2, 1, 3, 3, 3, 3, 2, 1, 4, 4, 4, 4, 3, 2, 1, 4, 4, 4, 4, 4, 3, 2, 1, 5, 5, 5, 5, 5, 4, 3, 2, 1, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 6, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums = A001318, general pentagonal numbers: (1, 2, 5, 12, 15, 22,...).

Eigensequence of the triangle = A168259: (1, 2, 6, 14, 38, 96, 254, 656,...).

LINKS

Table of n, a(n) for n=1..78.

FORMULA

Triangle by Rows, A097806 * A111967; A097806 = the signed pairwise operator

(1's in the main diagonal, -1's in the adjacent diagonal and the rest zeros.)

a(n) = min(A004736,A204164); a(n)=min(j,floor((t+2)/2)), where j=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Apr 18 2013

EXAMPLE

First few rows of the triangle =

1;

1, 1;

2, 2, 1;

2, 2, 2, 1;

3, 3, 3, 2, 1;

3, 3, 3, 3, 2, 1;

4, 4, 4, 4, 3, 2, 1;

4, 4, 4, 4, 4, 3, 2, 1;

5, 5, 5, 5, 5, 4, 3, 2, 1;

5, 5, 5, 5, 5, 5, 4, 3, 2, 1;

6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1;

6, 6, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1;

7, 7, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1;

7, 7, 7, 7, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1;

8, 8, 8, 8, 8, 8, 8, 8, 7, 6, 5, 4, 3, 2, 1;

...

CROSSREFS

Cf. A001318, A097806, A111967, A168259, A004736, A204164.

Sequence in context: A256911 A107260 A279346 * A116204 A291592 A159905

Adjacent sequences:  A168255 A168256 A168257 * A168259 A168260 A168261

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 21 2009

STATUS

approved

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Last modified October 20 20:24 EDT 2019. Contains 328273 sequences. (Running on oeis4.)