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Search: id:A099425
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| A099425 |
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Expansion of (1+x^2)/(1-2*x-x^2). |
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+0
5
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| 1, 2, 6, 14, 34, 82, 198, 478, 1154, 2786, 6726, 16238, 39202, 94642, 228486, 551614, 1331714, 3215042, 7761798, 18738638, 45239074, 109216786, 263672646, 636562078, 1536796802, 3710155682, 8957108166, 21624372014, 52205852194
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A094024(n+1).
a(n) is the number of matchings of the corona C'(n) of the cycle graph C(n) and the complete graph K(1); in other words, C'(n) is the graph constructed from C(n) to which for each vertex v a new vertex v' and the edge vv' is added. Example: a(3)=14 because in the graph with vertex set {A,B,C,a,b,c} and edge set {AB,AC,BC,Aa,Bb,Cc} we have the following 14 matchings: the empty set, the six singletons containing one of the edges, {Aa,BC},{Bb,AC},{Cc,AB},{Aa,Bb},{Aa,Cc}, {Bb,Cc} and {Aa,Bb,Cc}. Row sums of A102413. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 07 2005
Apart from first term, same as A002203. - Peter Shor, May 12 2005.
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FORMULA
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a(n)=(1+sqrt(2))^n+(1-sqrt(2))^n-0^n; a(n)=a(n)=sum{k=0..n, A000129(n+1-k)C(1, k/2)(1+(-1)^k)/2}. a(n)=2*A001333(n)-0^n.
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CROSSREFS
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Cf. A102413.
Sequence in context: A070933 A059570 A018016 this_sequence A105635 A025257 A110152
Adjacent sequences: A099422 A099423 A099424 this_sequence A099426 A099427 A099428
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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), Oct 15 2004
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