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A342636 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 7*a(n) + a(n+1).

%I A342636 #9 Mar 30 2021 19:04:46
%S A342636 0,1,1,8,1,15,8,57,1,22,15,113,8,113,57,400,1,29,22,169,15,218,113,
%T A342636 799,8,169,113,848,57,799,400,2801,1,36,29,225,22,323,169,1198,15,323,
%U A342636 218,1639,113,1590,799,5601,8,225,169,1296,113,1639,848,5993,57,1198,799,5993,400,5601,2801
%N A342636 a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 7*a(n) + a(n+1).
%H A342636 Alois P. Heinz, <a href="/A342636/b342636.txt">Table of n, a(n) for n = 0..16384</a>
%F A342636 G.f.: x * Product_{k>=0} (1 + x^(2^k) + 7*x^(2^(k+1))).
%p A342636 a:= proc(n) option remember; `if`(n<2, n, (q->
%p A342636      `if`(d=1, 7*a(q)+a(q+1), a(q)))(iquo(n, 2, 'd')))
%p A342636     end:
%p A342636 seq(a(n), n=0..62);  # _Alois P. Heinz_, Mar 17 2021
%t A342636 a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], a[n/2], 7 a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 62}]
%t A342636 nmax = 62; CoefficientList[Series[x Product[(1 + x^(2^k) + 7 x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%Y A342636 Cf. A002487, A116528, A178243, A342603, A342633, A342634, A342635, A342637, A342638.
%K A342636 nonn
%O A342636 0,4
%A A342636 _Ilya Gutkovskiy_, Mar 17 2021