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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A256248

Adjacent sequences:  A215252 A215253 A215254 * A215256 A215257 A215258

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Aug 14 2012

STATUS

approved

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Last modified February 28 01:54 EST 2020. Contains 332319 sequences. (Running on oeis4.)