A119469 Triangle read by rows: row n gives coefficients (lowest degree first) of P_n(x), where P_0(x) = P_1(x) = 1; P_n(x) = P_{n-1}(x) + x^(n-2)*P_{n-2}(x).

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

Offset

0,3

Comments

P_n(x) has degree A002620(n).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..9549 (rows n=0..49 of triangle, flattened).

Example

Triangle begins:
1
1
2
2,1
2,1,2
2,1,2,2,1
2,1,2,2,3,1,2
2,1,2,2,3,3,3,2,2,1
2,1,2,2,3,3,5,3,4,3,3,1,2
2,1,2,2,3,3,5,5,5,5,5,4,5,3,2,2,1

Maple

P[0]:=1; P[1]:=1; d:=[0, 0]; M:=14; for n from 2 to M do P[n]:=expand(P[n-1]+q^(n-2)*P[n-2]);
lprint(seriestolist(series(P[n], q, M^2))); d:=[op(d), degree(P[n], q)]; od: d;

Crossrefs

A variant of A127836.

Rows converge to A003113.

Sequence in context: A245977 A082389 A246127 * A127439 A218775 A370558

Adjacent sequences: A119466 A119467 A119468 * A119470 A119471 A119472

Keyword

nonn,tabf

Author

N. J. A. Sloane, Apr 10 2007

Status

approved