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A342635 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 5*a(n) + a(n+1).

%I A342635 #11 Mar 30 2021 19:03:19
%S A342635 0,1,1,6,1,11,6,31,1,16,11,61,6,61,31,156,1,21,16,91,11,116,61,311,6,
%T A342635 91,61,336,31,311,156,781,1,26,21,121,16,171,91,466,11,171,116,641,61,
%U A342635 616,311,1561,6,121,91,516,61,641,336,1711,31,466,311,1711,156,1561,781,3906,1,31,26
%N A342635 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 5*a(n) + a(n+1).
%H A342635 Alois P. Heinz, <a href="/A342635/b342635.txt">Table of n, a(n) for n = 0..16384</a>
%F A342635 G.f.: x * Product_{k>=0} (1 + x^(2^k) + 5*x^(2^(k+1))).
%F A342635 a(n) == 1 (mod 5) for n >= 1. - _Hugo Pfoertner_, Mar 17 2021
%p A342635 a:= proc(n) option remember; `if`(n<2, n, (q->
%p A342635      `if`(d=1, 5*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))
%p A342635     end:
%p A342635 seq(a(n), n=0..66);  # _Alois P. Heinz_, Mar 17 2021
%t A342635 a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 5 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 66}]
%t A342635 nmax = 66; CoefficientList[Series[x Product[(1 + x^(2^k) + 5 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%Y A342635 Cf. A002487, A116528, A178243, A342603, A342633, A342634, A342636, A342637, A342638.
%K A342635 nonn
%O A342635 0,4
%A A342635 _Ilya Gutkovskiy_, Mar 17 2021