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A147610 a(n) = 3^(wt(n-1)-1), where wt() = A000120().

%I A147610 #14 Mar 24 2020 06:29:20
%S A147610 1,1,3,1,3,3,9,1,3,3,9,3,9,9,27,1,3,3,9,3,9,9,27,3,9,9,27,9,27,27,81,
%T A147610 1,3,3,9,3,9,9,27,3,9,9,27,9,27,27,81,3,9,9,27,9,27,27,81,9,27,27,81,
%U A147610 27,81,81,243,1,3,3,9,3,9,9,27,3,9,9,27,9,27,27,81,3,9,9,27,9,27,27,81,9
%N A147610 a(n) = 3^(wt(n-1)-1), where wt() = A000120().
%C A147610 a(n) = A147582(n)/4.
%H A147610 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polca030.jpg">Illustration of initial terms (Overlapping squares)</a> [From _Omar E. Pol_, Nov 15 2009]
%F A147610 a(n) = 3^A048881(n-2). - _R. J. Mathar_, Apr 30 2009
%F A147610 Recurrence: Write n = 2^i + 1 + j, 0 <= j < 2^i. Then a(2^i+1) = 1; for j>0, a(2^i+j+1) = 3*a(j+1). - _N. J. A. Sloane_, Jun 09 2009
%F A147610 G.f.: x*(Product_{k>=0} (1 + 3*x^(2^k)) - 1)/3. - _N. J. A. Sloane_, Jun 10 2009
%e A147610 When written as a triangle:
%e A147610 .1,
%e A147610 .1,3,
%e A147610 .1,3,3,9,
%e A147610 .1,3,3,9,3,9,9,27,
%e A147610 .1,3,3,9,3,9,9,27,3,9,9,27,9,27,27,81,
%e A147610 .1,3,3,9,3,9,9,27,3,9,9,27,9,27,27,81,3,9,9,27,9,27,27,81,9,27,27,81,27,81,81,243,
%e A147610 ....
%e A147610 Rows converge to A048883. Row sums give A000302. Partial sums give A151920.
%p A147610 A000120 := proc(n) local a,d; a := 0 ; for d from 0 to ilog2(n) do a := a+ ( floor(n/2^d) mod 2) ; od: a ; end: A048881 := proc(n) A000120(n+1)-1 ; end: A147610 := proc(n) 3^A048881(n) ; end: seq(A147610(n),n=0..100) ; # _R. J. Mathar_, Apr 30 2009
%t A147610 a[n_] := 3^(DigitCount[n - 1, 2, 1] - 1);
%t A147610 a /@ Range[2, 100] (* _Jean-François Alcover_, Mar 24 2020 *)
%o A147610 (PARI) a(n) = 3^(hammingweight(n-1)-1); \\ _Michel Marcus_, Mar 24 2020
%Y A147610 Cf. A048883, A000120, A000302, A151920, A147582, A048881.
%Y A147610 Cf. A079314. - _Omar E. Pol_, Nov 15 2009
%K A147610 nonn
%O A147610 2,3
%A A147610 _N. J. A. Sloane_, Apr 29 2009
%E A147610 Extended by _R. J. Mathar_, Apr 30 2009
%E A147610 Offset corrected by _N. J. A. Sloane_, Jun 09 2009
%E A147610 Further edited by _N. J. A. Sloane_, Aug 06 2009