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A002574 Restricted partitions.
(Formerly M1070 N0404)
8
0, 0, 1, 1, 2, 4, 7, 13, 24, 42, 76, 137, 245, 441, 792, 1420, 2550, 4576, 8209, 14732, 26433, 47424, 85092, 152670, 273914, 491453, 881744, 1581985, 2838333, 5092398, 9136528, 16392311, 29410243, 52766343, 94670652, 169853138, 304741614, 546751437, 980952673, 1759973660 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=3 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 and 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)=13 compositions 8=p(1)+p(2)+...+p(m) with p(1)=3 and p(k) <= 2*p(k+1):
[ 1] [ 3 1 1 1 1 1 ]
[ 2] [ 3 1 1 1 2 ]
[ 3] [ 3 1 1 2 1 ]
[ 4] [ 3 1 2 1 1 ]
[ 5] [ 3 1 2 2 ]
[ 6] [ 3 2 1 1 1 ]
[ 7] [ 3 2 1 2 ]
[ 8] [ 3 2 2 1 ]
[ 9] [ 3 2 3 ]
[10] [ 3 3 1 1 ]
[11] [ 3 3 2 ]
[12] [ 3 4 1 ]
[13] [ 3 5 ]
(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(3, 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[3, n]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 05 2013, after Maple *)
CROSSREFS
Sequence in context: A327543 A096236 A356932 * A069765 A090427 A006745
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Michael Somos
STATUS
approved

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