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A048574
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Self-convolution of 1 2 3 5 7 11 15 22 30 42 56 77 ... (A000041).
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4
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1, 4, 10, 22, 43, 80, 141, 240, 397, 640, 1011, 1568, 2395, 3604, 5360, 7876, 11460, 16510, 23588, 33418, 47006, 65640, 91085, 125596, 172215, 234820, 318579, 430060, 577920, 773130, 1030007, 1366644, 1806445, 2378892, 3121835, 4082796
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| 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
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 804
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FORMULA
| 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
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EXAMPLE
| a(4) = 22 because (1,2,3,5)*(5,3,2,1) = 5 + 6 + 6 + 5 = 22
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MAPLE
| 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
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MATHEMATICA
| a[n_] := First[ ListConvolve[ pp = Array[ PartitionsP, n], pp]]; Table[ a[n], {n, 1, 36}] (* From Jean-François Alcover, Oct 21 2011 *)
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CROSSREFS
| A000041, A000712, A023626.
Essentially the same as A052837.
Sequence in context: A034357 A023626 * A052837 A052821 A023628 A004798
Adjacent sequences: A048571 A048572 A048573 * A048575 A048576 A048577
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com)
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Sep 29 2000
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