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
Examples
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.
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).
Programs
-
Mathematica
Table[(8 + i)*2^(i - 10), {i, 10, 50}]
-
PARI
Vec(-2*x^10*(17*x-9)/(2*x-1)^2 + O(x^100)) \\ Colin Barker, Sep 29 2015
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)
Comments