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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..59.

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

FORMULA

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

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)). [Colin Barker, Jul 22 2012]

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

MATHEMATICA

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

CROSSREFS

Sequence in context: A138101 A287089 A095790 * A053910 A105074 A208847

Adjacent sequences: A109471 A109472 A109473 * A109475 A109476 A109477

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)