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

Author

N. J. A. Sloane, Apr 10 2007

Keywords

• nonn
• tabf

Comments

P_n(x) has degree A002620(n).

Examples

			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
		

Links

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

Crossrefs

A variant of A127836.

Rows converge to A003113.

Programs

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;