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A083323
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An alternating sum of decreasing powers.
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8
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1, 2, 6, 20, 66, 212, 666, 2060, 6306, 19172, 58026, 175100, 527346, 1586132, 4766586, 14316140, 42981186, 129009092, 387158346, 1161737180, 3485735826, 10458256052, 31376865306, 94134790220, 282412759266, 847255055012
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A000225 (if this starts 1,1,3,7....).
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 intersecting and for which either x is a proper subset of y or y is a proper subset of x, or 1) x = y. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008 Ross
Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if either 0) x is not a subset of y and y is not a subset of x and x and y are disjoint, or 1) x equals y. Then a(n) = |R|. [From Ross La Haye (rlahaye(AT)new.rr.com), Mar 19 2009]
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REFERENCES
| 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
| a(n)=3^n-2^n+1^n G.f. (1-4x+5x^2)/((1-x)(1-2x)(1-3x)) E.g.f. exp(3x)-exp(2x)+exp(x)
Row sums of triangle A134319. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 19 2007
a(n) = 2*StirlingS2(n+1,3) + StirlingS2(n+1,2) + 1. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 10 2008 Ross
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CROSSREFS
| Cf. A134319.
Cf. A028243, A000079.
Sequence in context: A148474 A156831 A027061 * A174846 A111285 A052991
Adjacent sequences: A083320 A083321 A083322 * A083324 A083325 A083326
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 27 2003
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