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Search: id:A094374
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| 1, 3, 8, 21, 56, 153, 428, 1221, 3536, 10353, 30548, 90621, 269816, 805353, 2407868, 7207221, 21588896, 64701153, 193972388, 581655021, 1744440776, 5232273753, 15694724108, 47079978021, 141231545456, 423677859153, 1271000023028
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OFFSET
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0,2
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COMMENT
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Binomial transform of A094373.
Row sums of A125103. - Paul Barry (pbarry(AT)wit.ie), Dec 04 2007
Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 2) x = y. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2008
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REFERENCES
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Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]
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FORMULA
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G.f.: (1-3x+x^2)/((1-x)(1-2x)(1-3x)); a(n)=6a(n-1)-11a(n-2)+6a(n-3). a(n)=A003462(n)+A000079(n).
a(n)=sum{k=0..n, C(n,k)+2^k*C(n,k+1)}; - Paul Barry (pbarry(AT)wit.ie), Dec 04 2007
a(n) = StirlingS2(n+1,3) + 2*StirlingS2(n+1,2) + 1. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 11 2008
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CROSSREFS
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Cf. A000225, A000392, A000079.
Sequence in context: A090413 A128105 A085560 this_sequence A008909 A006835 A014318
Adjacent sequences: A094371 A094372 A094373 this_sequence A094375 A094376 A094377
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 28 2004
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