

A276055


Number of palindromic compositions of n with parts in {1,2,4,6,8,10,...}.


2



1, 1, 2, 1, 4, 2, 7, 3, 13, 6, 23, 10, 42, 19, 75, 33, 136, 61, 244, 108, 441, 197, 793, 352, 1431, 638, 2576, 1145, 4645, 2069, 8366, 3721, 15080, 6714, 27167, 12087, 48961, 21794, 88215, 39254, 158970, 70755, 286439, 127469, 516164, 229725, 930072
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OFFSET

0,3


REFERENCES

S. Heubach and T. Mansour, Combinatorics of Compositions and Words, CRC Press, 2010.


LINKS

Table of n, a(n) for n=0..46.
V. E. Hoggatt, Jr., and Marjorie Bicknell, Palindromic compositions, Fibonacci Quart., Vol. 13(4), 1975, pp. 350356.


FORMULA

G.f.: g(z) =(1+z^2 )*(1+zz^3)/(1z^22z^4+z^6). In the more general situation of compositions into a[1]<a[2]<a[3]<..., denoting F(z) = Sum(z^{a[j]},j>=1}, we have g(z)=(1+F(z))/(1F(z^2)) (see Theorem 1.2 in the Hoggatt et al. reference).


EXAMPLE

a(6) = 7 because the palindromic compositions of 6 with parts in {1,2,4,6,8,...} are 6, 141, 222, 2112, 1221, 11211, and 111111.


MAPLE

g := (1+z^2)*(1+zz^3)/(1z^22*z^4+z^6): gser:= series(g, z=0, 55): seq(coeff(gser, z, n), n=0..50);


MATHEMATICA

CoefficientList[Series[(1 + x^2) (1 + x  x^3)/(1  x^2  2 x^4 + x^6), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2016 *)


CROSSREFS

Cf. A028495, A276053,
Sequence in context: A143375 A074364 A256610 * A252866 A008796 A254594
Adjacent sequences: A276052 A276053 A276054 * A276056 A276057 A276058


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Aug 17 2016


STATUS

approved



