OFFSET
3,2
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
LINKS
Harry J. Smith, Table of n, a(n) for n = 3..200
Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-6).
FORMULA
a(n) = 11/2 - n - 2^(n+1) + (1/2)*3^n.
G.f.: 2*x^4*(5-6*x)/((1-x)^2*(1-2*x)*(1-3*x)). - Colin Barker, Feb 17 2012
EXAMPLE
a(4)=10 because each of the 5 (=A000111(4)) up-down permutations and 5 down-up permutations has 3 sequences. For example, the 3 sequences of 2413 are 24, 41, and 13. - Emeric Deutsch, Jul 11 2009
MAPLE
n3 := n->11/2-n-2^(n+1)+1/2*3^n; seq(n3(i), i=3..30);
MATHEMATICA
Table[11/2-n-2^(n+1)+3^n/2, {n, 3, 30}]
PROG
(PARI) { for (n=3, 200, write("b060157.txt", n, " ", (3^n + 11)/2 - 2^(n + 1) - n); ) } \\ Harry J. Smith, Jul 02 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Mar 12 2001
STATUS
approved