cp's OEIS Frontend

A309019 Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1)) + x^(2^(k+2))).

%I A309019 #6 Jul 06 2019 20:59:15
%S A309019 0,1,1,2,1,4,2,4,1,7,4,7,2,10,4,7,1,12,7,12,4,18,7,13,2,19,10,16,4,21,
%T A309019 7,12,1,20,12,20,7,31,12,23,4,34,18,29,7,38,13,22,2,34,19,31,10,45,16,
%U A309019 30,4,41,21,32,7,40,12,20,1,33,20,33,12,52,20,39,7,58,31,50,12,66,23,39,4,61,34,56,18,81,29,54,7,74,38
%N A309019 Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1)) + x^(2^(k+2))).
%F A309019 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n-1) + a(n) + a(n+1).
%t A309019 nmax = 90; CoefficientList[Series[x Product[(1 + x^(2^k) + x^(2^(k + 1)) + x^(2^(k + 2))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%t A309019 a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], a[(n - 3)/2] + a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 90}]
%Y A309019 Cf. A002487, A309020, A309021, A309022.
%K A309019 nonn
%O A309019 0,4
%A A309019 _Ilya Gutkovskiy_, Jul 06 2019