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A007307
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a(n) = a(n-2) + a(n-3).
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5
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0, 1, 2, 1, 3, 3, 4, 6, 7, 10, 13, 17, 23, 30, 40, 53, 70, 93, 123, 163, 216, 286, 379, 502, 665, 881, 1167, 1546, 2048, 2713, 3594, 4761, 6307, 8355, 11068, 14662, 19423, 25730, 34085, 45153, 59815, 79238, 104968, 139053, 184206, 244021, 323259, 428227
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OFFSET
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0,3
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COMMENTS
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Also the number of maximal matchings in the (n-2)-pan graph. - Eric W. Weisstein, Dec 30 2017
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
Eric Weisstein's World of Mathematics, Pan Graph
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1).
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FORMULA
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a(n) = p(n-1) + 2*p(n-2) = p(n+1) + p(n-2), with p(n):=A000931(n+3). O.g.f: x*(1+2*x)/(1-x^2-x^3). - Wolfdieter Lang, Jun 15 2010
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MAPLE
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G(x):=(-1-x^3)/(-1+x^2+x^3): f[0]:=G(x): for n from 1 to 58 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n]/n!, n=1..43); # Zerinvary Lajos, Mar 27 2009
# second Maple program:
a:= n-> (<<0|1|0>, <0|0|1>, <1|1|0>>^n.<<($0..2)>>)[1$2]:
seq(a(n), n=0..60); # Alois P. Heinz, Nov 06 2016
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MATHEMATICA
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Join[{a=0, b=1, c=2}, Table[d=a+b; a=b; b=c; c=d, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Feb 26 2011 *)
Table[- RootSum[-1 - # + #^3 &, -16 #^n - 13 #^(n + 1) + #^(n + 2) &]/23, {n, 20}] (* Eric W. Weisstein, Dec 30 2017 *)
LinearRecurrence[{0, 1, 1}, {1, 3, 3}, 20] (* Eric W. Weisstein, Dec 30 2017 *)
CoefficientList[Series[x (-1 - 3 x - 2 x^2)/(-1 + x^2 + x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 30 2017 *)
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PROG
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(MAGMA) I:=[0, 1, 2]; [n le 3 select I[n] else Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jun 09 2013
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CROSSREFS
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Sequence in context: A032303 A032215 A117363 * A207617 A141576 A078019
Adjacent sequences: A007304 A007305 A007306 * A007308 A007309 A007310
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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