|
| |
|
|
A325849
|
|
Number of strict compositions of n with no three consecutive parts in arithmetic progression.
|
|
9
|
|
|
|
1, 1, 1, 3, 3, 5, 9, 13, 19, 23, 51, 57, 91, 117, 179, 283, 381, 531, 737, 1017, 1335, 2259, 2745, 3983, 5289, 7367, 9413, 13155, 19461, 25129, 33997, 45633, 61225, 80481, 107091, 137475, 205243, 253997, 345527, 447003, 604919, 768331, 1026167, 1299227
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
A composition of n is a finite sequence of positive integers with sum n. a(n) is the number of strict compositions of n with no two of their adjacent first-differences equal, or with no 0's in their second-differences.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
The a(1) = 1 through a(8) = 19 compositions:
(1) (2) (3) (4) (5) (6) (7) (8)
(12) (13) (14) (15) (16) (17)
(21) (31) (23) (24) (25) (26)
(32) (42) (34) (35)
(41) (51) (43) (53)
(132) (52) (62)
(213) (61) (71)
(231) (124) (125)
(312) (142) (134)
(214) (143)
(241) (152)
(412) (215)
(421) (251)
(314)
(341)
(413)
(431)
(512)
(521)
|
|
|
MATHEMATICA
|
Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&], !MemberQ[Differences[#, 2], 0]&]], {n, 0, 30}]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
