|
| |
|
|
A048887
|
|
Array T read by antidiagonals, where T(m,n)=number of compositions of n into parts <= m.
|
|
14
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 20 2010: Taking finite differences of array columns from the top down, we obtain
(1; 1,1; 1,2,1; 1,4,2,1;...) = A048004 rows.
|
|
|
REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Princeton University Press, Princeton, NJ, 1978, p. 154.
|
|
|
FORMULA
| G.f.: (1-z)/[1-2z+z^(t+1)].
|
|
|
EXAMPLE
| 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,...
|
|
|
MAPLE
| 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);
|
|
|
CROSSREFS
| Rows: A000045 (Fibonacci), A000073 (tribonacci), A000078 (Tetranacci), etc.
Essentially a reflected version of A092921. See A048004 and A126198 for closely related arrays.
Cf. A048004 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 20 2010]
Sequence in context: A004070 A180562 A199711 * A047913 A152977 A117935
Adjacent sequences: A048884 A048885 A048886 * A048888 A048889 A048890
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
|
| |
|
|
