A338739 Number of true-palindromic compositions of n.

1, 2, 2, 4, 4, 8, 8, 16, 16, 31, 32, 62, 63, 124, 126, 248, 252, 496, 504, 991, 1007, 1982, 2013, 3960, 4023, 7914, 8040, 15816, 16068, 31609, 32112, 63171, 64180, 126251, 128266, 252318, 256347, 504268, 512324, 1007801, 1023909, 2014131, 2046338, 4025329, 4089724

Offset

1,2

Comments

A true-palindromic composition or true-palindrome to be a composition whose digit-comma-sequence is the same whether read from left to right or right to left. [Shapcott p. 35]

Links

Table of n, a(n) for n=1..45.

Caroline Shapcott, An introduction to true-palindromic compositions, Australasian Journal of Combinatorics, Volume 60(1) (2014), Pages 35-49.

Formula

Shapcott gives a g.f on p. 3, and 1 should be subtracted to get sequence for n>=1.

Example

(12, 6, 21) is a true-palindromic composition of 39.
(126, 621) is a true-palindromic composition of 747.

Prog

(PARI) rev(n) = Vecrev(n=digits(n)); \\ A004086
ispal(n) = Vecrev(n=digits(n))==n; \\ A002113
radd(n) = fromdigits(Vecrev(digits(n))) + n; \\ A056964
lista(nn) = my(x='x+O('x^(nn))); Vec(sum(k=0, nn, if (ispal(k), x^k))/(1 - sum(k=1, nn, if (k%10, x^radd(k)))) - 1);

Crossrefs

Cf. A002113, A004086, A056964.

Cf. A016116 (symmetric compositions), A338740.

Sequence in context: A378360 A263614 A082267 * A076939 A117575 A131572

Adjacent sequences: A338736 A338737 A338738 * A338740 A338741 A338742

Keyword

nonn,base

Author

Michel Marcus, Nov 06 2020

Status

approved