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
Vincenzo Librandi, Table of n, a(n) for n = 1..500
Shimon Even & Abraham Lempel, Generation and enumeration of all solutions of the characteristic sum condition, Information and Control 21 (1972), 476-482.
H. Minc, A problem in partitions: Enumeration of elements of a given degree in the free commutative entropic cyclic groupoid, Proc. Edinburgh Math. Soc. (2) 11 1958/1959 223-224.
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved