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A342615 a(0) = 0, a(1) = 1; a(2*n) = 9*a(n), a(2*n+1) = a(n) + a(n+1).

%I A342615 #10 May 04 2023 19:06:10
%S A342615 0,1,9,10,81,19,90,91,729,100,171,109,810,181,819,820,6561,829,900,
%T A342615 271,1539,280,981,919,7290,991,1629,1000,7371,1639,7380,7381,59049,
%U A342615 7390,7461,1729,8100,1171,2439,1810,13851,1819,2520,1261,8829,1900,8271,8209,65610,8281,8919,2620
%N A342615 a(0) = 0, a(1) = 1; a(2*n) = 9*a(n), a(2*n+1) = a(n) + a(n+1).
%H A342615 Robert Israel, <a href="/A342615/b342615.txt">Table of n, a(n) for n = 0..10000</a>
%F A342615 G.f.: x * Product_{k>=0} (1 + 9*x^(2^k) + x^(2^(k+1))).
%p A342615 N:= 100: # for a(0) to a(N)
%p A342615 g:= x*mul(1+9*x^(2^k)+x^(2^(k+1)),k=0..ilog2(N)):
%p A342615 S:= series(g,x,N+1):
%p A342615 seq(coeff(S,x,i),i=0..N); # _Robert Israel_, May 04 2023
%t A342615 a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], 9 a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 51}]
%t A342615 nmax = 51; CoefficientList[Series[x Product[(1 + 9 x^(2^k) + x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%Y A342615 Cf. A002487, A178569, A178590, A237711, A244643, A342610, A342611, A342614.
%K A342615 nonn,look
%O A342615 0,3
%A A342615 _Ilya Gutkovskiy_, Mar 16 2021