A079862 a(i) = the number of occurrences of 9's in the palindromic compositions of n=2*i-1 = the number of occurrences of 10's in the palindromic compositions of n=2*i.

18, 38, 80, 168, 352, 736, 1536, 3200, 6656, 13824, 28672, 59392, 122880, 253952, 524288, 1081344, 2228224, 4587520, 9437184, 19398656, 39845888, 81788928, 167772160, 343932928, 704643072, 1442840576, 2952790016, 6039797760, 12348030976, 25232932864

Offset

10,1

Comments

This sequence is part of a family of sequences, namely R(n,k), the number of ks 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 >= 2k.

Links

Colin Barker, Table of n, a(n) for n = 10..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(n) = (n+8)*2^(n-10).

From Colin Barker, Sep 29 2015: (Start)

a(n) = 2*A159697(n-10).

a(n) = 4*a(n-1) - 4*a(n-2) for n>11.

G.f.: -2*x^10*(17*x-9) / (2*x-1)^2.

(End)

Example

a(10) = 18 since the palindromic compositions of 19 that contain a 9 are 9+1+9 and the 16 compositions of the form c+9+(reverse of c), where c represents a composition of 5.

Mathematica

Table[(8 + i)*2^(i - 10), {i, 10, 50}]

Prog

(PARI) Vec(-2*x^10*(17*x-9)/(2*x-1)^2 + O(x^100)) \\ Colin Barker, Sep 29 2015

Crossrefs

Cf. A057711, A001792, A079859, A078836, A079861, A079863.

Sequence in context: A190739 A084585 A132761 * A106521 A070686 A043118

Adjacent sequences: A079859 A079860 A079861 * A079863 A079864 A079865

Keyword

easy,nonn

Author

Silvia Heubach (sheubac(AT)calstatela.edu), Jan 11 2003

Status

approved