OFFSET
0,3
COMMENTS
A composition of n is a finite sequence of positive integers summing to n.
The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (3,1,2) are (-2,1).
LINKS
EXAMPLE
The a(1) = 1 through a(8) = 20 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)
(121) (41) (42) (43) (44)
(1111) (131) (51) (52) (53)
(212) (123) (61) (62)
(11111) (141) (151) (71)
(222) (232) (161)
(321) (313) (242)
(1212) (12121) (323)
(2121) (1111111) (1232)
(111111) (1313)
(2123)
(2222)
(2321)
(3131)
(3212)
(21212)
(11111111)
MATHEMATICA
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], SameQ@@Abs[Differences[#]]&]], {n, 0, 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, s)={my(R=matid(n), t=0); while(R, R=step(R, n, s); t+=vecsum(R[n, ])); t}
a(n) = {numdiv(max(1, n)) + sum(s=1, n-1, w(n, 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