|
| |
|
|
A007971
|
|
INVERT transform of central trinomial coefficients (A002426).
|
|
8
| |
|
|
0, 1, 2, 2, 4, 8, 18, 42, 102, 254, 646, 1670, 4376, 11596, 31022, 83670, 227268, 621144, 1706934, 4713558, 13072764, 36398568, 101704038, 285095118, 801526446, 2259520830, 6385455594, 18086805002, 51339636952, 146015545604
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| For n>1, a(n) = 2(A005043(n-1)+A005043(n-2)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 06 2003
Number of paths of a walk on the integers, allowing steps of size 0, +1, and -1, which return to the starting point for the first time at time n. [From David P. Sanders (dps(AT)fciencias.unam.mx), May 04 2009]
|
|
|
FORMULA
| A002426(n) = Sum_{i=1..n} a(i)*A002426(n-i), n>0.
G.f.: 1-sqrt(1-2*x-3*x^2).
a(0)=0, a(1)=1, a(2)=2, then a(n)= (1/2) *(a(1)*a(n-1)+a(2)*a(n-2)+....+a(n-1)*a(1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 24 2003
a(n)=2^(1-n)*sum(binomial(k,n-k)*a000108(k-1)*3^(n-k),k,1,n), n>0
[Kruchinin (kru(AT)ie.tusur.ru), Feb 05 2011]
G.f.: 1-sqrt(1-2*x-3*(x^2))= x/G(0) ; G(k) = 1-2*x/(1+x/(1+x/(1-2*x/(1-x/(2-x/G(k+1)))))) ; (continued fraction). - Sergei N. Gladkovskii, Dec 11 2011
|
|
|
CROSSREFS
| Cf. A002426. A001006(n)=A007971(n+2)/2.
Cf. A025227.
Sequence in context: * A126068 A167022 A168055 A005702 A095335 A100396
Adjacent sequences: A007968 A007969 A007970 * A007972 A007973 A007974
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| David Dumas (dumas(AT)TCNJ.EDU)
|
| |
|
|
