OFFSET
0,8
COMMENTS
A composition S with sum n and length k is anti-palindromic if S(i) != S(k+1-i) for 1 <= i < floor(k). - Andrew Howroyd, Feb 28 2023
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..3467 (rows 0..100)
George E. Andrews, Matthew Just, and Greg Simay, Anti-palindromic compositions, arXiv:2102.01613 [math.CO], 2021. Also Fib. Q., 60:2 (2022), 164-176. See Table 2.
FORMULA
G.f.: A(x,y) = (1 + x*y/(1 - x))/(1 - 2*x^3*y^2/((1 + x)*(1 - x)^2)). - Andrew Howroyd, Feb 28 2023
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1,
0, 1, 2;
0, 1, 2, 2;
0, 1, 4, 4;
0, 1, 4, 8, 4;
0, 1, 6, 12, 8, 4;
0, 1, 6, 18, 20, 12;
...
PROG
(PARI) T(n)=[Vecrev(p) | p<-Vec((1 + x*y/(1 - x))/(1 - 2*x^3*y^2/((1 + x)*(1 - x)^2)) + O(x*x^n))]
{ my(rows=T(12)); for(i=1, #rows, print(rows[i])) } \\ Andrew Howroyd, Feb 28 2023
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jul 13 2022
EXTENSIONS
Terms a(33) and beyond from Andrew Howroyd, Feb 28 2023
STATUS
approved