OFFSET
1,1
LINKS
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(n) = 3 + 4*(n-2-floor((n-3)/4)).
From Wesley Ivan Hurt, Jul 15 2015: (Start)
G.f.: x*(3+4*x+4*x^3+x^4)/((x-1)^2*(1+x+x^2+x^3)).
a(n) = a(n-1)+a(n-4)-a(n-5), n>5.
a(n) = (6*n-1+(-1)^n-2*(-1)^((2*n+1-(-1)^n)/4))/2. (End)
MAPLE
MATHEMATICA
CoefficientList[Series[(3 + 4 x + 4 x^3 + x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Jul 15 2015 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {3, 7, 7, 11, 15}, 70] (* Vincenzo Librandi, Jul 16 2015 *)
PROG
(Magma) [3+4*(n-2-Floor((n-3)/4)) : n in [1..100]]; // Wesley Ivan Hurt, Jul 15 2015
(PARI) main(size)={my(v=vector(size), i, j); v[1]=3; for(j=2, size, x=0; for(i=1, j-1, if(v[i]==j, x=1; break)); if(x==1, v[j]=v[j-1], v[j]=v[j-1]+4)); return(v); } /* Anders Hellström, Jul 15 2015 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane and Benoit Cloitre, Mar 20 2003
STATUS
approved