6,1

a(n) = the number of occurrences of 5s in the palindromic compositions of 2n-1 = the number of occurrences of 6s in the palindromic compositions of 2n.

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, A079859, A079861 - A079863. 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.

P. Chinn, R. Grimaldi and S. Heubach, The frequency of summands of a particular size ..., Ars Combin. 69 (2003), 65-78.

a(6)=6 since the palindromic compositions of 11 that contain a 5 are 3+5+3, 1+2+5+2+1, 2+1+5+1+2, 1+1+1+5+1+1+1 and 5+1+5, for a total of 6 5s. The palindromic compositions of 12 that contain a 6 are 3+6+3, 1+2+6+2+1, 2+1+6+1+2, 1+1+1+6+1+1+1 and 6+6.

Table[i*2^(i-6), {i, 6, 50}]

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

Sequence in context: A143702 A134067 A024932 this_sequence A142875 A074981 A066510

Adjacent sequences: A078833 A078834 A078835 this_sequence A078837 A078838 A078839

easy,nonn

Silvia Heubach (sheubac(AT)calstatela.edu), Jan 17 2003