OFFSET
1,6
COMMENTS
Number of compositions n=p(1)+p(2)+...+p(m) with p(1)=4 and p(k) <= 2*p(k+1), see example. [Joerg Arndt, Dec 18 2012]
REFERENCES
Minc, H.; 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.
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(9)=13 compositions 9=p(1)+p(2)+...+p(m) with p(1)=4 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(4, 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}]]]; Table[v[4, n], {n, 1, 40}] (* Jean-François Alcover, Jan 10 2014, translated from Maple *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Michael Somos
STATUS
approved