|
Search: id:A072863
|
|
|
| A072863 |
|
Binomial transform of n^2/2 - n/2 + 1. |
|
+0
5
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Number of 123-avoiding ternary words of length n-1.
|
|
LINKS
|
P. Braendeen and T. Mansour, Finite automata and pattern avoidance in words
|
|
FORMULA
|
f[n_, 1] := n^2/2 - n/2 + 1; f[n_, m_] := f[n, m] = f[n, m - 1] + f[n + 1, m - 1].
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
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
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
|
|
MATHEMATICA
|
Table[Sum[Binomial[m-1, k](#^2/2 -#/2 +1 &)[k+1], {k, 0, m}], {m, 36}]
|
|
CROSSREFS
|
Cf. A134247, A000124.
Sequence in context: A048470 A138237 A121286 this_sequence A054963 A118046 A057153
Adjacent sequences: A072860 A072861 A072862 this_sequence A072864 A072865 A072866
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael A. Childers (childers_moof(AT)yahoo.com), Jul 27 2002
|
|
EXTENSIONS
|
Corrected and extended by Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jul 30 2002
|
|
|
Search completed in 0.004 seconds
|
