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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

P. Chinn, R. Grimaldi and S. Heubach, The Frequency of Summands of a Particular Size in Palindromic Compositions, Ars Combin. 69 (2003), 65-78.

Index entries for linear recurrences with constant coefficients, signature (4,-4).

FORMULA

a(i) = (2+i)*2^(i-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

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 August 8 08:26 EDT 2020. Contains 336293 sequences. (Running on oeis4.)