A032526 a(n) = floor(5*n^2/2).

0, 2, 10, 22, 40, 62, 90, 122, 160, 202, 250, 302, 360, 422, 490, 562, 640, 722, 810, 902, 1000, 1102, 1210, 1322, 1440, 1562, 1690, 1822, 1960, 2102, 2250, 2402, 2560, 2722, 2890, 3062, 3240, 3422, 3610, 3802, 4000, 4202, 4410, 4622, 4840, 5062

Offset

0,2

Links

Table of n, a(n) for n=0..45.

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

Formula

a(n) = 2n^2 + floor(n^2/2). - Wesley Ivan Hurt, Jun 14 2013

From Bruno Berselli, Jun 14 2013: (Start)

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

a(n) = 2*A032527(n). (End)

Sum_{n>=1} 1/a(n) = Pi^2/60 + tan(Pi/(2*sqrt(5)))*Pi/(2*sqrt(5)). - Amiram Eldar, Aug 15 2025

Maple

A032526:=n->floor(5*n^2/2): seq(A032526(n), n=0..100); # Wesley Ivan Hurt, Feb 03 2017

Mathematica

Table[Floor[5 n^2/2], {n, 0, 50}] (* Bruno Berselli, Jun 14 2013 *)
LinearRecurrence[{2, 0, -2, 1}, {0, 2, 10, 22}, 50] (* Harvey P. Dale, Dec 14 2016 *)

Prog

(Magma) [Floor(5*n^2/2): n in [0..50]]; // Bruno Berselli, Jun 14 2013

Crossrefs

Cf. A032527.

Sequence in context: A065450 A090288 A331132 * A294538 A096183 A218612

Adjacent sequences: A032523 A032524 A032525 * A032527 A032528 A032529

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved