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 A052471 Number of noncaterpillar trees on n nodes (A000055-A005418). 2
 0, 0, 0, 0, 0, 0, 1, 3, 11, 34, 99, 279, 773, 2103, 5661, 15160, 40373, 107355, 285059, 757273, 2013177, 5361100, 14303274, 38250297, 102538714, 275597098, 742674804, 2006661720, 5436008057, 14763754746, 40196603110, 109703958381, 300091975184, 822705857129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Caterpillar MAPLE with(numtheory): b:= proc(n) option remember; `if`(n<=1, n,       (add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))     end: a:= n-> b(n) -(add(b(k) *b(n-k), k=0..n)-`if`(irem(n, 2)=0,         b(n/2), 0))/2 -ceil(2^(n-4) + 2^(iquo(n-2, 2)-1)): seq(a(n), n=1..40); # Alois P. Heinz, May 18 2013 MATHEMATICA b[n_] := b[n] = If[n <= 1, n, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n - j], {j, 1, n-1}])/(n-1)]; a[n_] := b[n] - (Sum[b[k]*b[n-k], {k, 0, n}] - If[ Mod[n, 2] == 0, b[n/2], 0])/2 - Ceiling[2^(n-4) + 2^(Quotient[n-2, 2] - 1)]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Feb 19 2016, after Alois P. Heinz *) CROSSREFS Cf. A000055, A005418. Sequence in context: A247103 A036542 A084266 * A037496 A180762 A134326 Adjacent sequences:  A052468 A052469 A052470 * A052472 A052473 A052474 KEYWORD nonn AUTHOR EXTENSIONS a(14) and up from Eric W. Weisstein, Jul 17 2004. STATUS approved

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Last modified April 19 03:11 EDT 2019. Contains 322237 sequences. (Running on oeis4.)