This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A030118 #52 May 16 2025 15:46:09
%S A030118 1,1,2,4,6,7,7,7,8,10,12,13,13,13,14,16,18,19,19,19,20,22,24,25,25,25,
%T A030118 26,28,30,31,31,31,32,34,36,37,37,37,38,40,42,43,43,43,44,46,48,49,49,
%U A030118 49,50,52,54,55,55,55,56,58,60,61,61,61,62,64,66,67,67,67,68,70,72,73
%N A030118 a(0) = 1, a(1) = 1, a(n) = a(n-1) - a(n-2) + n.
%C A030118 Contains all positive integers except for 3 mod 6 and 5 mod 6 (A047270). - _Jon Perry_, Nov 02 2014
%H A030118 Robert Israel, <a href="/A030118/b030118.txt">Table of n, a(n) for n = 0..10000</a>
%H A030118 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,3,-1).
%F A030118 a(
%F A030118 G.f.: (1-2*x+3*x^2-x^3)/((1-x+x^2)*(1-x)^2). - _Robert Israel_, Nov 02 2014
%F A030118 a(n) = n iff n is either 1 or 2 mod 6. - _Jon Perry_, Nov 02 2014
%F A030118 a(n) = n + 1 - ((-1)^floor((n-1)/3) + (-1)^floor(n/3))/2) = n + 1 - A010892(n+5). - _G. C. Greubel_, Jul 24 2019
%F A030118 For k >= 1, a(6*k-1) = a(6*k) = a(6*k+1) = 6*k+1; a(6*k+2) = 6*k+2; a(6*k+3) = 6*k+4; a(6*k+4) = 6*k+6. - _Bernard Schott_, Jul 24 2019
%F A030118 a(n) = 3*a(n-1) - 4*a(n-2) + 3*a(n-3) - a(n-4) for n > 3. - _Chai Wah Wu_, Jun 30 2020
%p A030118 A:= gfun:-rectoproc({a(n)=a(n-1)-a(n-2)+n , a(0)=1,a(1)=1},a(n),remember):
%p A030118 seq(A(n),n=0..80); # _Robert Israel_, Nov 02 2014
%t A030118 Table[n+1 -((-1)^Floor[(n-1)/3] +(-1)^Floor[n/3])/2, {n, 0, 80}] (* _G. C. Greubel_, Jul 24 2019 *)
%t A030118 nxt[{n_,a_,b_}]:={n+1,b,b-a+n+1}; NestList[nxt,{1,1,1},80][[;;,2]] (* or *) LinearRecurrence[{3,-4,3,-1},{1,1,2,4},80] (* _Harvey P. Dale_, May 16 2025 *)
%o A030118 (Sage) [lucas_number1(n+1,2,1)-lucas_number1(n,1,1) for n in range(0, 80)] # _Zerinvary Lajos_, Nov 10 2009
%o A030118 (Magma) [1] cat [n le 2 select (n) else n + Self(n-1)-Self(n-2): n in [1..80]]; // _Vincenzo Librandi_, Nov 02 2014
%o A030118 (PARI) vector(80, n, n--; n+1 - ((-1)^floor((n-1)/3) + (-1)^floor(n/3))/2) \\ _G. C. Greubel_, Jul 24 2019
%o A030118 (GAP) Concatenation([1], List([1..80], n-> n+1 - ((-1)^Int((n-1)/3) + (-1)^Int(n/3))/2 )); # _G. C. Greubel_, Jul 24 2019
%Y A030118 Cf. A010892, A047270.
%K A030118 nonn,easy
%O A030118 0,3
%A A030118 _Dragan Stevanovic_
%E A030118 More terms from _Erich Friedman_