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A002573 Restricted partitions.
(Formerly M1062 N0399)
9
0, 1, 1, 2, 4, 7, 12, 22, 39, 70, 126, 225, 404, 725, 1299, 2331, 4182, 7501, 13458, 24145, 43316, 77715, 139430, 250152, 448808, 805222, 1444677, 2591958, 4650342, 8343380, 14969239, 26856992, 48185362, 86451602, 155106844, 278284440, 499283177, 895787396, 1607174300, 2883507098 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=2 and p(k) <= 2*p(k+1), see example. [Joerg Arndt, Dec 18 2012]
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Shimon Even & Abraham Lempel, Generation and enumeration of all solutions of the characteristic sum condition, Information and Control 21 (1972), 476-482.
EXAMPLE
From Joerg Arndt, Dec 18 2012: (Start)
There are a(8)=22 compositions 8=p(1)+p(2)+...+p(m) with p(1)=2 and p(k) <= 2*p(k+1):
[ 1] [ 2 1 1 1 1 1 1 ]
[ 2] [ 2 1 1 1 1 2 ]
[ 3] [ 2 1 1 1 2 1 ]
[ 4] [ 2 1 1 2 1 1 ]
[ 5] [ 2 1 1 2 2 ]
[ 6] [ 2 1 2 1 1 1 ]
[ 7] [ 2 1 2 1 2 ]
[ 8] [ 2 1 2 2 1 ]
[ 9] [ 2 1 2 3 ]
[10] [ 2 2 1 1 1 1 ]
[11] [ 2 2 1 1 2 ]
[12] [ 2 2 1 2 1 ]
[13] [ 2 2 2 1 1 ]
[14] [ 2 2 2 2 ]
[15] [ 2 2 3 1 ]
[16] [ 2 2 4 ]
[17] [ 2 3 1 1 1 ]
[18] [ 2 3 1 2 ]
[19] [ 2 3 2 1 ]
[20] [ 2 3 3 ]
[21] [ 2 4 1 1 ]
[22] [ 2 4 2 ]
(End)
MAPLE
v := proc(c, d) option remember; local i; if d < 0 or c < 0 then 0 elif d = c then 1 else add(v(i, d-c), i=1..2*c); fi; end; [ seq(v(2, n), n=1..50) ];
MATHEMATICA
v[c_, d_] := v[c, d] = If[d < 0 || c < 0, 0, If[d == c, 1, Sum[v[i, d - c], {i, 1, 2*c}]]]; a[n_] := v[2, n]; Table[a[n], {n, 1, 35}] (* Jean-François Alcover, Jan 30 2012, after Maple *)
CROSSREFS
A column of the triangle in A176431.
Sequence in context: A289153 A289019 A254685 * A288317 A064492 A000072
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)