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 A072863 a(n) = 2^(n-3)*(n^2+3*n+8). 7
 1, 3, 9, 26, 72, 192, 496, 1248, 3072, 7424, 17664, 41472, 96256, 221184, 503808, 1138688, 2555904, 5701632, 12648448, 27918336, 61341696, 134217728, 292552704, 635437056, 1375731712, 2969567232, 6392119296, 13723762688 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of 1+n*(n+1)/2, A000124. Number of 123-avoiding ternary words of length n-1. Row sums of triangle A134247. Also double binomial transform of (1, 1, 1, 0, 0, 0,...). - Gary W. Adamson, Oct 15 2007 Equals row sums of triangle A144333. - Gary W. Adamson, Sep 18 2008 LINKS P. Braendeen and T. Mansour, Finite automata and pattern avoidance in words Tosic R., Masulovic D., Stojmenovic I., Brunvoll J., Cyvin B. N. and Cyvin S. J., Enumeration of polyhex hydrocarbons to h = 17, J. Chem. Inf. Comput. Sci., 1995, 35, 181-187, Table 1, with an error at h=16. Index entries for linear recurrences with constant coefficients, signature (6,-12,8) FORMULA G.f. : (1-3x+3x^2)/(1-2x)^3; a(n)=2^(n-3)(n^2+3n+8). - Paul Barry, Jul 22 2004 E.g.f.: e^(2*x)*(1+x+x^2/2); a(n)=sum{k=0..2, C(n,k)*2^(n-k)}. - Paul Barry, Mar 27 2007 a(n-1) + A001788(n-2) = A104270(n). - R. J. Mathar, May 21 2018 MAPLE A072863 := proc(n)     2^(n-3)*(n^2+3*n+8) ; end proc: # R. J. Mathar, May 21 2018 MATHEMATICA Table[Sum[Binomial[m-1, k](#^2/2 -#/2 +1 &)[k+1], {k, 0, m}], {m, 36}] PROG (PARI) a(n)=2^(n-3)*(n^2+3*n+8); \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A134247, A000124, A144333. Sequence in context: A048470 A138237 A121286 * A054963 A291733 A118046 Adjacent sequences:  A072860 A072861 A072862 * A072864 A072865 A072866 KEYWORD nonn,easy AUTHOR Michael A. Childers (childers_moof(AT)yahoo.com), Jul 27 2002 EXTENSIONS Corrected and extended by Wouter Meeussen, Jul 30 2002 Title and offset corrected. - R. J. Mathar, May 21 2018 New name using explicit formula. - Joerg Arndt, May 21 2018 STATUS approved

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Last modified February 21 19:40 EST 2019. Contains 320376 sequences. (Running on oeis4.)