A167499 a(n) = n*(n+3)/2 + 6.

6, 8, 11, 15, 20, 26, 33, 41, 50, 60, 71, 83, 96, 110, 125, 141, 158, 176, 195, 215, 236, 258, 281, 305, 330, 356, 383, 411, 440, 470, 501, 533, 566, 600, 635, 671, 708, 746, 785, 825, 866, 908, 951, 995, 1040, 1086, 1133, 1181, 1230, 1280, 1331, 1383, 1436, 1490

Offset

0,1

Comments

Numbers m > 5 such that 8*m - 39 is a square. - Bruce J. Nicholson, Jul 25 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, Journal of Integer Sequences, Vol. 22 (2019), Article 19.8.4.

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

Formula

a(n) = n + a(n-1) + 1, with n > 1, a(1) = 8.

From Vincenzo Librandi, Sep 16 2013: (Start)

G.f.: (6 - 10*x + 5*x^2)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

Sum_{n>=0} 1/a(n) = 2*Pi*tanh(Pi*sqrt(39)/2)/sqrt(39) - 1/5. - Amiram Eldar, Jan 17 2021

From Elmo R. Oliveira, Oct 31 2024: (Start)

E.g.f.: exp(x)*(6 + 2*x + x^2/2).

a(n) = A187710(n+1)/2. (End)

Maple

A167499:=n->n*(n+3)/2+6: seq(A167499(n), n=0..100); # Wesley Ivan Hurt, Jul 25 2017

Mathematica

Table[n*(n + 3)/2 + 6, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *)
CoefficientList[Series[(6 - 10 x + 5 x^2) / (1 - x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Sep 16 2013 *)
LinearRecurrence[{3, -3, 1}, {6, 8, 11}, 60] (* Harvey P. Dale, Jun 21 2022 *)

Prog

(Magma) [n*(n+3)/2+6: n in [0..60]]; // Vincenzo Librandi, Sep 16 2013
(PARI) a(n)=n*(n+3)/2+6 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A187710.

Sequence in context: A315855 A287408 A287398 * A020716 A020937 A183208

Adjacent sequences: A167496 A167497 A167498 * A167500 A167501 A167502

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 07 2009

Status

approved