A183857 a(n) = n - 1 + ceiling((2/3)*n^2); complement of A183874.

1, 4, 8, 14, 21, 29, 39, 50, 62, 76, 91, 107, 125, 144, 164, 186, 209, 233, 259, 286, 314, 344, 375, 407, 441, 476, 512, 550, 589, 629, 671, 714, 758, 804, 851, 899, 949, 1000, 1052, 1106, 1161, 1217, 1275, 1334, 1394, 1456, 1519, 1583, 1649, 1716, 1784, 1854, 1925, 1997, 2071

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Formula

a(n) = n - 1 + ceiling((2/3)*n^2).

From Elmo R. Oliveira, Apr 01 2026: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

G.f.: x*(1 + 2*x + x^2 + x^3 - x^4)/((1 - x^3)*(1 - x)^2). (End)

E.g.f.: (9 + exp(x)*(6*x^2 + 15*x - 7) - 2*exp(-x/2)*cos(sqrt(3)*x/2))/9. - Stefano Spezia, Apr 02 2026

Mathematica

a=3/2; b=0;
Table[n+Floor[(a*n+b)^(1/2)], {n, 100}]
Table[n-1+Ceiling[(n*n-b)/a], {n, 80}]
LinearRecurrence[{2, -1, 1, -2, 1}, {1, 4, 8, 14, 21}, 60] (* Harvey P. Dale, Apr 12 2020 *)

Crossrefs

Cf. A183874.

Sequence in context: A312698 A312699 A131937 * A088804 A374505 A344012

Adjacent sequences: A183854 A183855 A183856 * A183858 A183859 A183860

Keyword

nonn,easy

Author

Clark Kimberling, Jan 07 2011

Status

approved