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A338739
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Number of true-palindromic compositions of n.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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]
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LINKS
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FORMULA
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Shapcott gives a g.f on p. 3, and 1 should be subtracted to get sequence for n>=1.
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EXAMPLE
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(12, 6, 21) is a true-palindromic composition of 39.
(126, 621) is a true-palindromic composition of 747.
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PROG
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(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);
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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