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 A007307 a(n) = a(n-2) + a(n-3). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of maximal matchings in the (n-2)-pan graph. - Eric W. Weisstein, Dec 30 2017 LINKS 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). FORMULA 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 MAPLE 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A032303 A032215 A117363 * A207617 A141576 A078019 Adjacent sequences:  A007304 A007305 A007306 * A007308 A007309 A007310 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 10 08:09 EDT 2021. Contains 342845 sequences. (Running on oeis4.)