OFFSET
1,2
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
The circular differences of a composition c of length k are c_{i + 1} - c_i for i < k and c_1 - c_i for i = k. For example, the circular differences of (1,2,1,3) are (1,-1,2,-2).
LINKS
EXAMPLE
The a(1) = 1 through a(8) = 16 compositions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (12) (13) (14) (15) (16) (17)
(21) (22) (23) (24) (25) (26)
(111) (31) (32) (33) (34) (35)
(1111) (41) (42) (43) (44)
(11111) (51) (52) (53)
(222) (61) (62)
(1212) (1111111) (71)
(2121) (1232)
(111111) (1313)
(2123)
(2222)
(2321)
(3131)
(3212)
(11111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SameQ@@Abs[Differences[Append[#, First[#]]]]&]], {n, 15}]
PROG
(PARI)
step(R, n, s)={matrix(n, n, i, j, if(i>j, if(j>s, R[i-j, j-s]) + if(j+s<=n, R[i-j, j+s])) )}
w(n, k, s)={my(R=matrix(n, n, i, j, i==j&&abs(i-k)==s), t=0); while(R, R=step(R, n, s); t+=R[n, k]); t}
a(n) = {numdiv(max(1, n)) + sum(s=1, n-1, sum(k=1, n, w(n, k, s)))} \\ Andrew Howroyd, Aug 22 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 11 2019
EXTENSIONS
a(26)-a(42) from Lars Blomberg, May 30 2019
Terms a(43) and beyond from Andrew Howroyd, Aug 22 2019
STATUS
approved