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%I #10 Aug 22 2012 00:55:13
%S 1,1,2,3,4,6,10,13,23,29,42,65,107,136,243,308,444,687,1131,1439,2570,
%T 3257,4696,7266,11962,15219,27181,34447,49666,76847,126513,160960,
%U 287473,364320,525280,812753,1338033,1702353,3040386,3853139
%N 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.
%C If S is the binary representation of the decimal number N, then a(n) = A215244(N).
%C a(n) is an upper bound for A215245(n), which might be tight infinitely often.
%F 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.
%F 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).
%F 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).
%Y Cf. A215244, A215245, A215246, A215254.
%K nonn,base
%O 0,3
%A _N. J. A. Sloane_, Aug 14 2012
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