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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). 5

%I

%S 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,

%T 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,

%U 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

%N 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).

%C P_n(x) has degree A002620(n).

%H Seiichi Manyama, <a href="/A119469/b119469.txt">Table of n, a(n) for n = 0..9549 (rows n=0..49 of triangle, flattened).</a>

%e Triangle begins:

%e 1

%e 1

%e 2

%e 2,1

%e 2,1,2

%e 2,1,2,2,1

%e 2,1,2,2,3,1,2

%e 2,1,2,2,3,3,3,2,2,1

%e 2,1,2,2,3,3,5,3,4,3,3,1,2

%e 2,1,2,2,3,3,5,5,5,5,5,4,5,3,2,2,1

%p 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]);

%p lprint(seriestolist(series(P[n],q,M^2))); d:=[op(d),degree(P[n],q)]; od: d;

%Y A variant of A127836.

%Y Rows converge to A003113.

%K nonn,tabf

%O 0,3

%A _N. J. A. Sloane_, Apr 10 2007

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Last modified January 21 13:55 EST 2020. Contains 331113 sequences. (Running on oeis4.)