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%I #32 Aug 12 2022 11:38:00
%S 1,2,5,8,12,17,22,28,35,42,50,59,68,78,89,100,112,125,138,152,167,182,
%T 198,215,232,250,269,288,308,329,350,372,395,418,442,467,492,518,545,
%U 572,600,629,658,688,719,750,782,815,848,882,917,952,988,1025,1062,1100,1139,1178,1218,1259,1300,1342,1385,1428,1472,1517,1562,1608,1655,1702
%N a(1) = 1; for n > 1, a(n) = n - 1 + ceiling((n^2 - 1)/3); complement of A183860.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F a(n) = n - 1 + ceiling((n^2 - 1)/3).
%F a(n) = floor((2*n^2 + 6*n - 5)/6) for n > 1. - _Sela Fried_, Jul 12 2022
%F G.f.: x*(1 + 2*x^2 - x^3 + x^4 - x^5)/((1 - x)^3*(1 + x + x^2)). - _Stefano Spezia_, Jul 12 2022
%t a=3;b=1;
%t Table[n+Floor[(a*n+b)^(1/2)],{n,90}]
%t Table[n-1+Ceiling[(n*n-b)/a],{n,70}]
%t LinearRecurrence[{2,-1,1,-2,1},{1,2,5,8,12,17},70] (* _Harvey P. Dale_, Jul 01 2015 *)
%o (PARI) a(n) = if (n==1, 1, n - 1 + ceil((n^2 - 1)/3)); \\ _Michel Marcus_, Jul 13 2022
%o (PARI) a(n)=if(n==1, 1, n^2\3+n-1) \\ _Charles R Greathouse IV_, Jul 13 2022
%Y Cf. A183860.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jan 07 2011
%E Name corrected by _Michel Marcus_, Jul 13 2022
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