A082450 a(n) = 5*(n^2 - n + 2)/2.

5, 5, 10, 20, 35, 55, 80, 110, 145, 185, 230, 280, 335, 395, 460, 530, 605, 685, 770, 860, 955, 1055, 1160, 1270, 1385, 1505, 1630, 1760, 1895, 2035, 2180, 2330, 2485, 2645, 2810, 2980, 3155, 3335, 3520, 3710, 3905, 4105, 4310, 4520, 4735, 4955, 5180, 5410, 5645

Offset

0,1

Comments

Also the sum of five consecutive triangular numbers starting with A000217(-3). - Bruno Berselli, Jun 18 2015

References

Found on a quiz.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 5*n + a(n-1) - 5 for n>0, a(0)=5. - Vincenzo Librandi, Aug 08 2010

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2; a(0)=5, a(1)=5, a(2)=10. - Harvey P. Dale, Mar 23 2013

G.f.: 5*(1-2*x+2*x^2)/(1-x)^3. - Wesley Ivan Hurt, May 02 2021

From Elmo R. Oliveira, Dec 10 2025: (Start)

E.g.f.: 5*exp(x)*(x^2 + 2)/2.

a(n) = 5*A152947(n+1). (End)

Mathematica

Table[(5(n^2-n+2))/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {5, 5, 10}, 50] (* Harvey P. Dale, Mar 23 2013 *)

Prog

(PARI) a(n)=5*(n^2-n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [5*(n^2-n+2)/2 : n in [0..80]]; // Wesley Ivan Hurt, May 02 2021

Crossrefs

Essentially 5*A000124.

Cf. A000217, A152947.

Sequence in context: A242129 A022088 A245418 * A304266 A212344 A298181

Adjacent sequences: A082447 A082448 A082449 * A082451 A082452 A082453

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 25 2003

Status

approved