A342633 - OEIS

%I #9 Mar 30 2021 18:56:22

%S 0,1,1,4,1,7,4,13,1,10,7,25,4,25,13,40,1,13,10,37,7,46,25,79,4,37,25,

%T 88,13,79,40,121,1,16,13,49,10,67,37,118,7,67,46,163,25,154,79,241,4,

%U 49,37,136,25,163,88,277,13,118,79,277,40,241,121,364,1,19,16,61,13,88,49,157

%N a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 3*a(n) + a(n+1).

%H Alois P. Heinz, <a href="/A342633/b342633.txt">Table of n, a(n) for n = 0..16384</a>

%F G.f.: x * Product_{k>=0} (1 + x^(2^k) + 3*x^(2^(k+1))).

%p a:= proc(n) option remember; `if`(n<2, n, (q->

%p      `if`(d=1, 3*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))

%p     end:

%p seq(a(n), n=0..71);  # _Alois P. Heinz_, Mar 17 2021

%t a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 3 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 71}]

%t nmax = 71; CoefficientList[Series[x Product[(1 + x^(2^k) + 3 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

%Y Cf. A002487, A116528, A178243, A342603, A342634, A342635, A342636, A342637, A342638.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Mar 17 2021