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

Author

Michel Marcus, Nov 06 2020

Keywords

• nonn
• base

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]

Examples

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

Links

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

Crossrefs

Cf. A002113, A004086, A056964.

Cf. A016116 (symmetric compositions), A338740.

Programs

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);

Formula

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