A183861 a(1) = 1; for n > 1, a(n) = n - 1 + ceiling((n^2 - 1)/3); complement of A183860.

1, 2, 5, 8, 12, 17, 22, 28, 35, 42, 50, 59, 68, 78, 89, 100, 112, 125, 138, 152, 167, 182, 198, 215, 232, 250, 269, 288, 308, 329, 350, 372, 395, 418, 442, 467, 492, 518, 545, 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

Offset

1,2

Links

Table of n, a(n) for n=1..70.

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

Formula

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

a(n) = floor((2*n^2 + 6*n - 5)/6) for n > 1. - Sela Fried, Jul 12 2022

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

Mathematica

a=3; b=1;
Table[n+Floor[(a*n+b)^(1/2)], {n, 90}]
Table[n-1+Ceiling[(n*n-b)/a], {n, 70}]
LinearRecurrence[{2, -1, 1, -2, 1}, {1, 2, 5, 8, 12, 17}, 70] (* Harvey P. Dale, Jul 01 2015 *)

Prog

(PARI) a(n) = if (n==1, 1, n - 1 + ceil((n^2 - 1)/3)); \\ Michel Marcus, Jul 13 2022
(PARI) a(n)=if(n==1, 1, n^2\3+n-1) \\ Charles R Greathouse IV, Jul 13 2022

Crossrefs

Cf. A183860.

Sequence in context: A241566 A002960 A022942 * A024534 A011974 A049633

Adjacent sequences: A183858 A183859 A183860 * A183862 A183863 A183864

Keyword

nonn,easy

Author

Clark Kimberling, Jan 07 2011

Extensions

Name corrected by Michel Marcus, Jul 13 2022

Status

approved