Search: id:A072863
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%I A072863
%S A072863 1,3,9,26,72,192,496,1248,3072,7424,17664,41472,96256,221184,503808,
%T A072863 1138688,2555904,5701632,12648448,27918336,61341696,134217728,
%U A072863 292552704,635437056,1375731712,2969567232,6392119296,13723762688
%N A072863 Binomial transform of n^2/2 - n/2 + 1.
%C A072863 Number of 123-avoiding ternary words of length n-1.
%C A072863 Equals row sums of triangle A144333. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Sep 18 2008]
%H A072863 P. Braendeen and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0309269">
               Finite automata and pattern avoidance in words</a>
%F A072863 f[n_, 1] := n^2/2 - n/2 + 1; f[n_, m_] := f[n, m] = f[n, m - 1] + f[n 
               + 1, m - 1].
%F A072863 G.f. : (1-3x+3x^2)/(1-2x)^3; a(n)=2^(n-3)(n^2+3n+8). - Paul Barry (pbarry(AT)wit.ie), 
               Jul 22 2004
%F A072863 E.g.f.: e^(2x)*(1+x+x^2/2); a(n)=sum{k=0..2, C(n,k)*2^(n-k)} [offset 
               0]; - Paul Barry (pbarry(AT)wit.ie), Mar 27 2007
%F A072863 Row sums of triangle A134247. Also, binomial transform of A000124: (1, 
               2, 4, 7, 11, 16, 22, 29,...) and double binomial transform of (1, 
               1, 1, 0, 0, 0,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 
               15 2007
%p A072863 with(combstruct); gramm_Alkyl:=Alkyl=Prod(Carbon, Set(Alkyl, card<=1)), 
               Carbon=Atom: specs_Alkyl:=[Alkyl, {gramm_Alkyl}, unlabeled]: gramm_S1_Alkyl:=S1_Alkyl[X]=Union(Prod(Carbo\
               n, S1_Alkyl[X], Set(Alkyl, card<=1)), Prod(Prod(Carbon, X), Set(Alkyl, 
               card<=1))), X=Epsilon: specs_S1_Alkyl:=[S1_Alkyl[X], {gramm_S1_Alkyl, 
               gramm_Alkyl}, unlabeled]: gramm_S2b_Alkyl:=S2_Alkyl[X, X]=Union(Prod(Carbon, 
               S2_Alkyl[X, X], Set(Alkyl, card<=1)), Prod(Carbon, Union(Prod(S1_Alkyl[X], 
               S1_Alkyl[X]), Prod(S1_Alkyl[X], X), Prod(X, X)), Set(Alkyl, card<=1))): 
               specs_S2b_Alkyl:=[S2_Alkyl[X, X], {gramm_S2b_Alkyl, gramm_S1_Alkyl, 
               gramm_Alkyl}, unlabeled]: seq(count(specs_S2b_Alkyl, size=i), i=1..28); 
               # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 15 2009]
%t A072863 Table[Sum[Binomial[m-1, k](#^2/2 -#/2 +1 &)[k+1], {k, 0, m}], {m, 36}]
%Y A072863 Cf. A134247, A000124.
%Y A072863 A144333 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 18 2008]
%Y A072863 Sequence in context: A048470 A138237 A121286 this_sequence A054963 A118046 
               A057153
%Y A072863 Adjacent sequences: A072860 A072861 A072862 this_sequence A072864 A072865 
               A072866
%K A072863 nonn
%O A072863 1,2
%A A072863 Michael A. Childers (childers_moof(AT)yahoo.com), Jul 27 2002
%E A072863 Corrected and extended by Wouter Meeussen (wouter.meeussen(AT)pandora.be), 
               Jul 30 2002

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