OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).
FORMULA
a(2*k+1) = 4*k+3, a(4*k+2) = 4*k+1, a(4*k+4) = 2*k+2. - Ralf Stephan, Jun 10 2005
a(n) = (11*n+2-(5*n+6)*(-1)^n+(n-2)*(1+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4))/8. - Luce ETIENNE, Oct 29 2016
From Colin Barker, Oct 29 2016: (Start)
a(n) = 2*a(n-4) - a(n-8) for n>8.
G.f.: x*(3 + x + 7*x^2 + 2*x^3 + 5*x^4 + 3*x^5 + x^6)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2). (End)
EXAMPLE
G.f. = 3*x + x^2 + 7*x^3 + 2*x^4 + 11*x^5 + 5*x^6 + 15*x^7 + 4*x^8 + ...
PROG
(PARI) Vec(x*(3+x+7*x^2+2*x^3+5*x^4+3*x^5+x^6)/((1-x)^2*(1+x)^2*(1+x^2)^2) + O(x^100)) \\ Colin Barker, Oct 29 2016
(PARI) {a(n) = if( n%2, 2*n+1, n%4, n-1, n/2)}; /* Michael Somos, Nov 06 2016 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Oct 28 2001
STATUS
approved