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A397141
Number of palindromic Carlitz compositions of n with parts in standard order.
1
1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 4, 3, 3, 6, 4, 8, 11, 12, 14, 22, 20, 36, 39, 56, 58, 94, 88, 155, 155, 249, 250, 420, 395, 700, 666, 1142, 1104, 1908, 1802, 3184, 3017, 5271, 5041, 8814, 8364, 14738, 14033, 24574, 23578, 41175, 39515, 69057, 66533
OFFSET
0,14
LINKS
John Tyler Rascoe, PARI code.
EXAMPLE
a(16) = 4: (1,2,1,2,1,2,1,2,1,2,1), (1,2,1,3,2,3,1,2,1), (1,2,3,1,2,1,3,2,1), (1,2,3,4,3,2,1).
MAPLE
b:= proc(n, m, l) option remember; `if`(n<=m+1 and n>0 and n<>l, 1, 0)+
add(`if`(j=l, 0, b(n-2*j, max(m, j), j)), j=1..min(n/2, m+1))
end:
a:= n-> `if`(n=0, 1, b(n, 0$2)):
seq(a(n), n=0..58); # Alois P. Heinz, Aug 25 2026
PROG
(PARI) \\ see links
CROSSREFS
KEYWORD
nonn,new
AUTHOR
John Tyler Rascoe, Aug 24 2026
STATUS
approved