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Search: id:A128915
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| A128915 |
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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*P_{n-2}(x). |
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+0
2
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| 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 3, 4, 4, 4, 3, 3, 2, 2, 2, 1, 1
(list; graph; listen)
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OFFSET
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0,32
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COMMENT
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P_n(x) appears to have degree A035106(n).
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REFERENCES
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A. V. Sills, Finite Rogers-Ramanujan type identities, Electron. J. Combin., 10 (2003), Research Paper 13, 122 pp. See Identity 3-14, p. 25.
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EXAMPLE
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Triangle begins:
1
1
1,0,1
1,0,1,1
1,0,1,1,1,0,1
1,0,1,1,1,1,1,1,1
1,0,1,1,1,1,2,1,2,1,1,0,1
1,0,1,1,1,1,2,2,2,2,2,1,2,1,1,1
1,0,1,1,1,1,2,2,3,2,3,2,3,2,3,2,2,1,1,0,1
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MAPLE
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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*P[n-2]);
lprint(seriestolist(series(P[n], q, M^2))); d:=[op(d), degree(P[n], q)]; od: d;
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CROSSREFS
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Rows converge to A003114 (coefficients in expansion of the first Rogers-Ramanujan identities). Cf. A119469.
Rows converge to A003106. Cf. A127836, A119469.
Sequence in context: A037888 A052308 A116510 this_sequence A063995 A020951 A117118
Adjacent sequences: A128912 A128913 A128914 this_sequence A128916 A128917 A128918
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KEYWORD
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nonn,tabf
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AUTHOR
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njas, Apr 24 2007
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