A338740 -id:A338740 - cp's OEIS frontend

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

Michel Marcus, Nov 06 2020

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]

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

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

Cf. A002113, A004086, A056964.

Cf. A016116 (symmetric compositions), A338740.

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);

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

cp's OEIS Frontend

A338739 Number of true-palindromic compositions of n.

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