Search: id:A130665
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%I A130665
%S A130665 1,4,7,16,19,28,37,64,67,76,85,112,121,148,175,256,259,268,277,304,313,
%T A130665 340,367,448,457,484,511,592,619,700,781,1024,1027,1036,1045,1072,1081,
%U A130665 1108,1135,1216,1225,1252,1279,1360,1387,1468,1549,1792,1801,1828,1855
%N A130665 a(n) = Sum_{k=1..n} 3^wt(k), where wt() = A000120().
%C A130665 It appears that A147562 is the main entry for this sequence. [From Omar 
               E. Pol (info(AT)polprimos.com), Nov 08 2009]
%C A130665 It appears that A160410 is also the main entry for this sequence. [From 
               Omar E. Pol (info(AT)polprimos.com), Nov 12 2009]
%D A130665 D. E. Knuth, Problem submitted to Amer. Math. Monthly, Jun 18 2007.
%H A130665 O. E. Pol, <a href="http://www.polprimos.com/imagenespub/polca011">Illustration 
               of initial terms (Neighbors of the vertices)</a> [From Omar E. Pol 
               (info(AT)polprimos.com), Nov 08 2009]
%H A130665 O. E. Pol, <a href="http://www.polprimos.com/imagenespub/polca013">Illustration 
               of initial terms (Overlapping squares)</a> [From Omar E. Pol (info(AT)polprimos.com), 
               Nov 08 2009]
%H A130665 O. E. Pol, <a href="http://www.polprimos.com/imagenespub/polca015">Illustration 
               of initial terms (One-step bishop)</a> [From Omar E. Pol (info(AT)polprimos.com), 
               Nov 08 2009]
%F A130665 With a different offset: a(1) = 1; a(n) = max { 3*a(k)+a(n-k) | 1 <= 
               k <= n/2 }, for n>1.
%F A130665 a(2n+1) = 4a(n) and a(2n) = 3a(n-1)+a(n).
%F A130665 a(n) = (A147562(n+1)-1)*3/4 + 1. [From Omar E. Pol (info(AT)polprimos.com), 
               Nov 08 2009]
%F A130665 a(n) = A160410(n+1)/4. [From Omar E. Pol (info(AT)polprimos.com), Nov 
               12 2009]
%p A130665 u:=3; a[1]:=1; M:=30; for n from 1 to M do a[2*n] := (u+1)*a[n]; a[2*n+1] 
               := u*a[n] + a[n+1]; od; t1:=[seq( a[n], n=1..2*M )]; # Gives sequence 
               with a different offset
%Y A130665 Cf. A006046, A116520, A130667.
%Y A130665 Partial sums of A048883. - David Applegate, Jun 11 2009.
%Y A130665 Cf. A147562, A151920, A151922, A160412. [From Omar E. Pol (info(AT)polprimos.com), 
               Nov 08 2009]
%Y A130665 Cf. A160410. [From Omar E. Pol (info(AT)polprimos.com), Nov 12 2009]
%Y A130665 Sequence in context: A166700 A160715 A160120 this_sequence A101534 A110933 
               A067398
%Y A130665 Adjacent sequences: A130662 A130663 A130664 this_sequence A130666 A130667 
               A130668
%K A130665 nonn
%O A130665 0,2
%A A130665 N. J. A. Sloane (njas(AT)research.att.com), based on a message from D. 
               E. Knuth, Jun 23 2007
%E A130665 Simpler definition (and new offset) from David Applegate, Jun 11 2009

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