A167487 a(n) = n*(n + 3)/2 + 8.

8, 10, 13, 17, 22, 28, 35, 43, 52, 62, 73, 85, 98, 112, 127, 143, 160, 178, 197, 217, 238, 260, 283, 307, 332, 358, 385, 413, 442, 472, 503, 535, 568, 602, 637, 673, 710, 748, 787, 827, 868, 910, 953, 997, 1042, 1088, 1135, 1183, 1232, 1282, 1333, 1385, 1438, 1492

Offset: 0

Author

Vincenzo Librandi, Nov 07 2009

Keywords

• nonn
• easy

Comments

2*a(i) + 3 is prime for i = 0..14. - Vincenzo Librandi, Jun 01 2014

Numbers m >= 8 such that 8*m - 55 is a square. - Bruce J. Nicholson, Jul 26 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A167499.

Programs

Magma

[n*(n+3)/2+8: n in [0..60]]; // Vincenzo Librandi, Sep 16 2013

Mathematica

Table[n (n + 3)/2 + 8, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 03 2011 *)
CoefficientList[Series[(8 - 14 x + 7 x^2) / (1 - x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Sep 16 2013 *)
LinearRecurrence[{3,-3,1},{8,10,13},60] (* Harvey P. Dale, Jul 05 2020 *)

PARI

a(n)=n*(n+3)/2+8 \\ Charles R Greathouse IV, Jun 16 2017

Formula

a(n) = n + a(n-1) + 1 with n > 1, a(1)=10.

G.f.: (8 - 14*x + 7*x^2)/(1 - x)^3. - Vincenzo Librandi, Sep 16 2013

a(n) = Sum_{i=n-5..n+7} i*(i+1)/26. - Bruno Berselli, Oct 20 2016

Sum_{n>=0} 1/a(n) = -1/7 + 2*Pi*tanh(sqrt(55)*Pi/2)/sqrt(55). - Amiram Eldar, Dec 13 2022

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

E.g.f.: exp(x)*(8 + 2*x + x^2/2).

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