A283839 - OEIS

%I #17 Apr 05 2017 07:44:05

%S 1,3,6,12,24,42,76,136,240,424,753,1337,2388,4280,7706,13940,25332,

%T 46224,84696,155786,287574,532624,989554,1843744,3444389,6450369,

%U 12107004,22771642,42913116,81014528,153199818,290152952,550332614,1045234672,1987731140

%N Row sums of A283838.

%C a(n) is odd for n >= 8 and n in { A247375 }. - _Alois P. Heinz_, Mar 26 2017

%H Alois P. Heinz, <a href="/A283839/b283839.txt">Table of n, a(n) for n = 8..1000</a>

%H Stefano Bilotta, <a href="http://arxiv.org/abs/1605.03785">Variable-length Non-overlapping Codes</a>, arXiv preprint arXiv:1605.03785, 2016

%p b:= proc(n, l, c, k) option remember; `if`(n=0, l,

%p       b(n-1, 1-l, 1, k)+`if`(c=k-1, 0, b(n-1, l, c+1, k)))

%p     end:

%p a:= proc(n) option remember; `if`(n<8, 0, a(n-1)+

%p       add(b(n-2*k-1, 0, 1, k), k=3..floor(n/2)-1))

%p     end:

%p seq(a(n), n=8..60);  # _Alois P. Heinz_, Mar 26 2017

%t nMax = 60; gf[k_] := gf[k] = x^(2k)(x-x^k)^2 / ((1-x)(1-x^k)(1-2x+x^k)) + O[x]^(nMax+1); a[n_] := Sum[SeriesCoefficient[gf[k], n], {k, 3, Floor[ n/2] - 1}]; Table[a[n], {n, 8, nMax}] (* _Jean-François Alcover_, Apr 05 2017 *)

%Y Cf. A247375, A283838.

%K nonn

%O 8,2

%A _N. J. A. Sloane_, Mar 25 2017

%E More terms from _Alois P. Heinz_, Mar 26 2017