Search: id:A048574
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%I A048574
%S A048574 1,4,10,22,43,80,141,240,397,640,1011,1568,2395,3604,5360,7876,11460,
%T A048574 16510,23588,33418,47006,65640,91085,125596,172215,234820,318579,
%U A048574 430060,577920,773130,1030007,1366644,1806445,2378892,3121835,4082796
%N A048574 Self-convolution of 1 2 3 5 7 11 15 22 30 42 56 77 ... (A000041).
%C A048574 Number of proper partitions of n into parts of two kinds (i.e. both kinds 
               must be present). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Feb 08 2006
%H A048574 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=804">
               Encyclopedia of Combinatorial Structures 804</a>
%F A048574 a(0)=0, a(n) = A000712(n)-2*A000041(n) for n>0. a(n)=sum_{k=1}^{n-1} 
               A000041(k)*A000041(n-k). G.f. ((Product_{k>0} 1/(1-x^k))-1)^2 = (exp(Sum_{k>
               0} (x^k/(1-x^k)/k))-1)^2. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Feb 08 2006
%e A048574 a(4) = 22 because (1,2,3,5)*(5,3,2,1) = 5 + 6 + 6 + 5 = 22
%p A048574 spec := [S,{C=Sequence(Z,1 <= card),B=Set(C,1 <= card),S=Prod(B,B)},unlabeled]: 
               seq(combstruct[count](spec,size=n), n=0..20); - Frank Adams-Watters 
               (FrankTAW(AT)Netscape.net), Feb 08 2006
%Y A048574 A000041, A000712, A023626.
%Y A048574 Essentially the same as A052837.
%Y A048574 Sequence in context: A006001 A034357 A023626 this_sequence A052837 A052821 
               A023628
%Y A048574 Adjacent sequences: A048571 A048572 A048573 this_sequence A048575 A048576 
               A048577
%K A048574 easy,nice,nonn
%O A048574 2,2
%A A048574 Alford Arnold (Alford1940(AT)aol.com)
%E A048574 More terms from Larry Reeves (larryr(AT)acm.org), Sep 29 2000

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