A109474 a(1)=1, a(2)=3; thereafter, a(n) = least positive integer > a(n-1) and not equal to a(i)+a(j)+a(k) for 1<=i<=j<=k<=n-1.

1, 3, 4, 13, 14, 23, 24, 33, 34, 43, 44, 53, 54, 63, 64, 73, 74, 83, 84, 93, 94, 103, 104, 113, 114, 123, 124, 133, 134, 143, 144, 153, 154, 163, 164, 173, 174, 183, 184, 193, 194, 203, 204, 213, 214, 223, 224, 233, 234, 243, 244, 253, 254, 263, 264, 273, 274, 283, 284

Offset: 1

Author

Bela Bajnok (bbajnok(AT)gettysburg.edu), Aug 10 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A001622.

Programs

Mathematica

Join[{1},LinearRecurrence[{1,1,-1},{3,4,13},60]] (* Harvey P. Dale, Aug 19 2014 *)

Formula

a(n) = max{1, 5*n-9+2*(-1)^n}.

From Colin Barker, Jul 22 2012: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) for n>4.

G.f.: x*(1+2*x+7*x^3)/((1-x)^2*(1+x)). (End)

Conjecture: Except for the first term, a(n)=10*n-a(n-1)-23 (with a(2)=3). - Vincenzo Librandi, Dec 07 2010 [This is easily proved. - N. J. A. Sloane, Aug 07 2017]

Sum_{n>=1} (-1)^(n+1)/a(n) = 1 - sqrt(1-2/sqrt(5))*Pi/(10*phi) + log(phi)/(2*sqrt(5)) - log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

Extensions

Definition corrected by Bela Bajnok (bbajnok(AT)gettysburg.edu) and N. J. A. Sloane, Aug 07 2017