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A052516
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Number of pairs of sets of cardinality at least 3.
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1
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0, 0, 0, 0, 0, 0, 20, 70, 182, 420, 912, 1914, 3938, 8008, 16172, 32526, 65262, 130764, 261800, 523906, 1048154, 2096688, 4193796, 8388054, 16776614, 33553780, 67108160, 134216970
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OFFSET
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0,7
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..2000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 82
Index to sequences with linear recurrences with constant coefficients, signature (5,-9,7,-2).
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FORMULA
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E.g.f.: exp(x)^2-2*exp(x)-2*x*exp(x)-exp(x)*x^2+1+2*x+2*x^2+x^3+1/4*x^4
Recurrence: {a(1)=0, a(2)=0, (2*n+2)*a(n)+(-3*n+1)*a(n+1)+(n-1)*a(n+2), a(3)=1/16*_C[0], a(4)=5/16*_C[0], a(5)= _C[0], a(6)=20+21/8*_C[0]}.
G.f.: 2*x^6*(10-15*x+6*x^2)/(1-x)^3/(1-2*x). [Colin Barker, Feb 19 2012]
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MAPLE
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Pairs spec := [S, {S=Prod(B, B), B=Set(Z, 3 <= card)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
with (combstruct):ZL:=[S, {S=Sequence(U, card=r), U=Set(Z, card>=3)}, labeled]: seq(count(subs(r=2, ZL), size=m), m=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2007
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MATHEMATICA
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Table[Max[0, 2^n-n^2-n-2], {n, 0, 50}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
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PROG
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(PARI) a(n)=max(0, 2^n-n^2-n-2) \\ Charles R Greathouse IV, Nov 20 2011
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CROSSREFS
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Sequence in context: A153728 A071395 A053741 * A083873 A143854 A139241
Adjacent sequences: A052513 A052514 A052515 * A052517 A052518 A052519
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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