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 A079861 a(n) is the number of occurrences of 7's in the palindromic compositions of 2*n-1, or also, the number of occurrences of 8's in the palindromic compositions of 2*n. 8
 10, 22, 48, 104, 224, 480, 1024, 2176, 4608, 9728, 20480, 43008, 90112, 188416, 393216, 819200, 1703936, 3538944, 7340032, 15204352, 31457280, 65011712, 134217728, 276824064, 570425344, 1174405120, 2415919104, 4966055936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 8,1 COMMENTS This sequence is part of a family of sequences, namely R(n,k), the number of k's in palindromic compositions of n. See also A057711, A001792, A078836, A079861, A079862. General formula: R(n,k) = 2^(floor(n/2) - k) * (2 + floor(n/2) - k) if n and k have different parity and R(n,k) = 2^(floor(n/2) - k) * (2 + floor(n/2) - k + 2^(floor((k+1)/2 - 1)) otherwise, for n >= 2*k. LINKS Vincenzo Librandi, Table of n, a(n) for n = 8..1000 Phyllis Chinn, Ralph Grimaldi and Silvia Heubach, The Frequency of Summands of a Particular Size in Palindromic Compositions, Ars Combin., Vol. 69 (2003), pp. 65-78. Index entries for linear recurrences with constant coefficients, signature (4,-4). FORMULA a(n) = (2+n)*2^(n-8). a(n) = 2*A111297(n-6). - Colin Barker, Dec 16 2014 a(n) = 4*a(n-1) - 4*a(n-2). - Colin Barker, Dec 16 2014 G.f.: -2*x^8*(9*x-5) / (2*x-1)^2. - Colin Barker, Dec 16 2014 From Amiram Eldar, Jan 13 2021: (Start) Sum_{n>=8} 1/a(n) = 1024*log(2) - 447047/630. Sum_{n>=8} (-1)^n/a(n) = 261617/630 - 1024*log(3/2). (End) EXAMPLE a(8)=10 since the palindromic compositions of 15 that contain a 7 are 7+1+7, 4+7+4, 1+3+7+3+1, 3+1+7+1+3, 2+2+7+2+2, 1+1+1+1+7+1+1+1+1, 1+1+2+7+2+1+1, 1+2+1+7+1+2+1 and 2+1+1+7+1+1+2, for a total of 10 7's. MATHEMATICA Table[(2 + i)*2^(i - 8), {i, 8, 50}] PROG (Magma) [(2+n)*2^(n-8) : n in [8..40]]; // Vincenzo Librandi, Sep 22 2011 (PARI) Vec(-2*x^8*(9*x-5)/(2*x-1)^2 + O(x^100)) \\ Colin Barker, Dec 16 2014 CROSSREFS Cf. A057711, A001792, A079859, A061256, A079862, A079863, A111297. Sequence in context: A104867 A179877 A216048 * A014008 A219744 A246419 Adjacent sequences: A079858 A079859 A079860 * A079862 A079863 A079864 KEYWORD easy,nonn AUTHOR Silvia Heubach (sheubac(AT)calstatela.edu), Jan 11 2003 STATUS approved

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Last modified April 16 16:12 EDT 2024. Contains 371749 sequences. (Running on oeis4.)