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Search: id:A048887
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| A048887 |
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Array T by antidiagonals, where T(m,n)=number of compositions of n into parts all <=m. |
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15
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| 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 5, 1, 1, 2, 4, 7, 8, 1, 1, 2, 4, 8, 13, 13, 1, 1, 2, 4, 8, 15, 24, 21, 1, 1, 2, 4, 8, 16, 29, 44, 34, 1, 1, 2, 4, 8, 16, 31, 56, 81, 55, 1, 1, 2, 4, 8, 16, 32, 61, 108, 149, 89, 1, 1, 2, 4, 8, 16, 32, 63, 120
(list; table; graph; listen)
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OFFSET
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1,5
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Princeton University Press, Princeton, NJ, 1978, p. 154.
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FORMULA
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G.f.: (1-z)/[1-2z+z^(t+1)].
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EXAMPLE
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T(2,5) counts 11111,1112,1121,1211,2111,122,212,221, where "1211" abbreviates the composition 1+2+1+1. The array begins:
1,1,1,1,1,1,1,...
1,2,3,5,8,13,...
1,2,4,7,13,...
1,2,4,8,...
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MAPLE
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G := t->(1-z)/(1-2*z+z^(t+1)): T := (m, n)->coeff(series(G(m), z=0, 30), z^n): matrix(7, 12, T);
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CROSSREFS
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Rows: A000045 (Fibonacci), A000073 (tribonacci), A000078 (Tetranacci), etc.
Essentially a reflected version of A092921. See A048004 and A126198 for closely related arrays.
Adjacent sequences: A048884 A048885 A048886 this_sequence A048888 A048889 A048890
Sequence in context: A104763 A027751 A004070 this_sequence A047913 A117935 A103462
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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