Search: id:A062051
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%I A062051
%S A062051 1,1,1,2,2,2,3,3,3,5,5,5,7,7,7,9,9,9,12,12,12,15,15,15,18,18,18,23,23,
%T A062051 23,28,28,28,33,33,33,40,40,40,47,47,47,54,54,54,63,63,63,72,72,72,81,
%U A062051 81,81,93,93,93,105,105,105,117,117,117,132,132,132,147,147,147,162
%N A062051 Number of partitions of n into parts which are powers of 3.
%C A062051 Number of different partial sums of 1+[1,*3]+[1,*3]+..., where [1,*3] 
               means we can either add 1 or multiply by 3. E.g. a(6)=3 because we 
               have 6=1+1+1+1+1+1=(1+1)*3=1*3+1+1+1 - Jon Perry (perry(AT)globalnet.co.uk), 
               Jan 01 2004
%C A062051 Also number of partitions of n into distinct 3-smooth parts. E.g. a(10) 
               = #{9+1, 8+2, 6+4, 6+3+1, 4+3+2+1} = #{9+1, 3+3+3+1, 3+3+1+1+1+1, 
               3+1+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1} = 5. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 07 2005
%H A062051 M. Latapy, <a href="http://www.dmtcs.org/proceedings/">Partitions of 
               an integer into powers</a>, DMTCS Proceedings AA (DM-CCG), 2001, 
               215-228.
%F A062051 a(n)=A005704([n/3]).
%e A062051 a(4) = 2 and the partitions are 3+1, 1+1+1+1; a(9) = 5 and the partitions 
               are 9; 3+3+3; 3+3+1+1+1; 3+1+1+1+1+1+1; 1+1+1+1+1+1+1+1+1.
%o A062051 (PARI) { n=15; v=vector(n); for (i=1,n,v[i]=vector(2^(i-1))); v[1][1]=1; 
               for (i=2,n, k=length(v[i-1]); for (j=1,k, v[i][j]=v[i-1][j]+1; v[i][j+k]=v[i-1][j]*3)); 
               c=vector(n); for (i=1,n, for (j=1,2^(i-1), if (v[i][j]<=n, c[v[i][j]]++))); 
               c } (Jon Perry)
%Y A062051 A005704 with terms repeated 3 times. Cf. A000123, A018819.
%Y A062051 Cf. A000009, A003586, A105420, A039966.
%Y A062051 Cf. A018819, A023893, A105420, A106244, A131995.
%Y A062051 Sequence in context: A076973 A008649 A008650 this_sequence A108711 A029059 
               A035449
%Y A062051 Adjacent sequences: A062048 A062049 A062050 this_sequence A062052 A062053 
               A062054
%K A062051 nonn
%O A062051 0,4
%A A062051 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 06 2001
%E A062051 More terms from Larry Reeves (larryr(AT)acm.org), Jun 11 2001

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