A215255 Let S be the binary string consisting of the first n digits of (100101)*; a(n) = number of ways of writing S as a product of palindromes.

1, 1, 2, 3, 4, 6, 10, 13, 23, 29, 42, 65, 107, 136, 243, 308, 444, 687, 1131, 1439, 2570, 3257, 4696, 7266, 11962, 15219, 27181, 34447, 49666, 76847, 126513, 160960, 287473, 364320, 525280, 812753, 1338033, 1702353, 3040386, 3853139

Offset

0,3

Comments

If S is the binary representation of the decimal number N, then a(n) = A215244(N).

a(n) is an upper bound for A215245(n), which might be tight infinitely often.

Links

Table of n, a(n) for n=0..39.

Formula

Recurrence: For n >= 4, a(n) = a(n-1)+a(n-d), where d = [3,2,4,2,4,3] according as n == [0,1,2,3,4,5] mod 6; initial conditions a(0)=a(1)=a(2)=1, a(3)=2.

G.f.: (x^17+x^14+x^12+5*x^11+2*x^10-x^9+3*x^8+3*x^7+6*x^5+4*x^4+3*x^3+2*x^2+x+1)/(1-10*x^6-6*x^12-x^18).

a(n) ~ C * D^n, where D = 1.4815692... and C depends on n mod 6 (approximate values of C are [0.580722..., 0.6452899..., 0.554135..., 0.667994..., 0.571395..., 0.556061...], respectively).

Crossrefs

Cf. A215244, A215245, A215246, A215254.

Sequence in context: A288338 A121152 A229863 * A200928 A318558 A347867

Adjacent sequences: A215252 A215253 A215254 * A215256 A215257 A215258

Keyword

nonn,base

Author

N. J. A. Sloane, Aug 14 2012

Status

approved