OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
a(n) = n - 1 + ceiling((n^2)/3).
From Elmo R. Oliveira, Apr 01 2026: (Start)
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).
G.f.: x*(1 + x + x^3 - x^4)/((1 - x)^3*(1 + x + x^2)). (End)
E.g.f.: (9 + exp(x)*(3*x^2 + 12*x - 5) - 4*exp(-x/2)*cos(sqrt(3)*x/2))/9. - Stefano Spezia, Apr 02 2026
MATHEMATICA
a=3; b=0;
Table[n+Floor[(a*n+b)^(1/2)], {n, 100}]
Table[n-1+Ceiling[(n*n-b)/a], {n, 80}]
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Clark Kimberling, Jan 07 2011
STATUS
approved