OFFSET
1,2
COMMENTS
Previous name was: Fibonacci(n) as n runs through the quarter-squares. [this is misleading]
This recurrence arose when a middle schooler was asked to complete a number sequence, given six of the Fibonacci numbers (1,2,3,5,8,13) but not told about the Fibonacci sequence.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
FORMULA
a(n) = a(n-1) + 1 + A002620(n-2). For n<2: a(1)=1, a(2)=2. O.g.f.: x*(2*x^3-x^2-x+1)/((-1+x)^4*(x+1)). - R. J. Mathar, Dec 05 2007
a(n) = -1/16-3*n^2/8+17*n/12+n^3/12+(-1)^n/16. - R. J. Mathar, Jul 22 2009
EXAMPLE
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stewart Charles Cureton (sarah.cureton(AT)att.net), Oct 16 2003
EXTENSIONS
New name using formula by R. J. Mathar from Joerg Arndt, Feb 27 2023
STATUS
approved