OFFSET
1,2
COMMENTS
A143100 = (1, 3, 4, 6, 13, 30, 64, 129, ...).
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 1..1000
FORMULA
Binomial transform of A143097: (1, 2, 4, 3, 5, 7, 6, 8, 10, 9, 11, ...). a(n) = 2*a(n-1) + A143100(n-1).
G.f.: x*(5*x^4-7*x^3+5*x^2-3*x+1)/((1-x)*(x^2-x+1)*(1-2*x)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009; [corrected by R. J. Mathar, Sep 16 2009]
EXAMPLE
MAPLE
A143097 := proc(n) if(n<=1)then return n: elif(n mod 3 <= 1)then return n+1-2*(n mod 3): else return n: fi: end: A143099 := proc(n) return add(binomial(n-1, k-1)*A143097(k), k=1..n): end: seq(A143099(n), n=1..32); # Nathaniel Johnston, Apr 30 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jul 24 2008
STATUS
approved