OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(n) = 3*(n-1-floor((n-1)/4)) + (-1)^floor((n-1)/2).
From Wesley Ivan Hurt, Oct 17 2015: (Start)
G.f.: x*(1+3*x+x^2+3*x^3+x^4)/((x-1)^2*(1+x+x^2+x^3)).
a(n) = a(n-1)+a(n-4)-a(n-5) for n>5.
a(n) = (18*n-9+3*(-1)^n-2*(-1)^((2*n+1-(-1)^n)/4))/8. (End)
E.g.f.: (1/8)*(2*sin(x) - 2*cos(x) + 18*x*exp(x) + 3*exp(-x) - 9*exp(x) + 8). - G. C. Greubel, Oct 18 2015
MAPLE
seq(3*(n - floor(n/4)) + (-1)^floor(n/2), n=0..100);
MATHEMATICA
CoefficientList[Series[(1 + 3 x + x^2 + 3 x^3 + x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Oct 17 2015 *)
RecurrenceTable[{a[1] == 1, a[2] == 4, a[3] == 5, a[4] == 8, a[5] == 10 , a[n+5] == a[n+4] + a[n+1] - a[n] }, a, {n, 1, 100}] (* G. C. Greubel, Oct 18 2015 *)
PROG
(Magma) [(18*n-9+3*(-1)^n-2*(-1)^((2*n+1-(-1)^n) div 4))/8 : n in [1..100]]; // Wesley Ivan Hurt, Oct 17 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary Detlefs, Mar 18 2010
EXTENSIONS
Formula corrected by Gary Detlefs, Mar 19 2010
STATUS
approved