A082643 a(n) = ceiling(n*(n+1/2)/2).

0, 1, 3, 6, 9, 14, 20, 27, 34, 43, 53, 64, 75, 88, 102, 117, 132, 149, 167, 186, 205, 226, 248, 271, 294, 319, 345, 372, 399, 428, 458, 489, 520, 553, 587, 622, 657, 694, 732, 771, 810, 851, 893, 936, 979, 1024, 1070, 1117, 1164, 1213, 1263, 1314, 1365, 1418, 1472, 1527

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Formula

a(n) = +2*a(n-1) -a(n-2) +a(n-4) -2*a(n-5) +a(n-6). - R. J. Mathar, Mar 11 2012

G.f.: (x + x^2 + x^3 + x^5)/((1 - x)^2*(1 - x^4)). - Robert Israel, Dec 20 2017

a(n) = n*(n + 1)/2 - floor(n/4). - Bruno Berselli, Mar 04 2021

Maple

seq(ceil(n*(n+1/2)/2), n=0..100); # Robert Israel, Dec 20 2017

Mathematica

Table[Ceiling[(n (n + 1/2))/2], {n, 0, 60}] (* or *) LinearRecurrence[{2, -1, 0, 1, -2, 1}, {0, 1, 3, 6, 9, 14}, 60] (* Harvey P. Dale, May 24 2014 *)

Prog

(PARI) a(n) = ceil(n*(n+1/2)/2); \\ Altug Alkan, Dec 20 2017

Crossrefs

Cf. A038707.

Cf. A000217, A002265.

Sequence in context: A310169 A310170 A310171 * A310172 A227849 A135524

Adjacent sequences: A082640 A082641 A082642 * A082644 A082645 A082646

Keyword

nonn,easy

Author

N. J. A. Sloane, May 16 2003

Status

approved