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A183861 a(1) = 1; for n > 1, a(n) = n - 1 + ceiling((n^2 - 1)/3); complement of A183860. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)