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 A319863 a(2n) = a(n) + a(n+1) + n (n > 1), a(2n+1) = a(n) + a(n-1) + 1 (n >= 1) with a(0) = a(1) = 1 and a(2) = 2. 0

%I

%S 1,1,2,3,7,4,13,6,15,11,22,12,25,18,28,20,34,22,42,27,44,34,48,35,55,

%T 38,59,44,62,47,69,49,72,55,81,57,87,65,90,70,98,72,103,79,105,83,113,

%U 84,117,91,122,94,129,98,133,104,137,107,145,110,148,117,152

%N a(2n) = a(n) + a(n+1) + n (n > 1), a(2n+1) = a(n) + a(n-1) + 1 (n >= 1) with a(0) = a(1) = 1 and a(2) = 2.

%C A "convoluted recurrence".

%H J.-P. Allouche and J. Shallit, <a href="http://dx.doi.org/10.1016/0304-3975(92)90001-V">The ring of k-regular sequences</a>, Theoretical Computer Sci., 98 (1992), 163-197.

%H J.-P. Allouche and J. Shallit, <a href="http://dx.doi.org/10.1016/S0304-3975(03)00090-2">The ring of k-regular sequences, II</a>, Theoret. Computer Sci., 307 (2003), 3-29.

%H Math Stackexchange, <a href="https://math.stackexchange.com/questions/1045477/convoluted-recurrence-f2n-fnfn1n-f2n1-fnfn-11/1045523#1045523">convoluted recurrence: f(2n)=f(n)+f(n+1)+n,f(2n+1)=f(n)+f(n-1)+1</a>, November 30 2014.

%K nonn

%O 0,3

%A _Jeffrey Shallit_, Sep 29 2018

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)