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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES S. Heubach and T. Mansour, Combinatorics of Compositions and Words, CRC Press, 2010. LINKS V. E. Hoggatt, Jr., and Marjorie Bicknell, Palindromic compositions, Fibonacci Quart., Vol. 13(4), 1975, pp. 350-356. FORMULA G.f.: g(z) =(1+z^2 )*(1+z-z^3)/(1-z^2-2z^4+z^6). In the more general situation of compositions into a[1]=1}, we have g(z)=(1+F(z))/(1-F(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+z-z^3)/(1-z^2-2*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

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)