A166136 a(n) = n*(n+3)/2 + 7.

9, 12, 16, 21, 27, 34, 42, 51, 61, 72, 84, 97, 111, 126, 142, 159, 177, 196, 216, 237, 259, 282, 306, 331, 357, 384, 412, 441, 471, 502, 534, 567, 601, 636, 672, 709, 747, 786, 826, 867, 909, 952, 996, 1041, 1087, 1134, 1182, 1231, 1281, 1332, 1384, 1437

Offset: 1

Author

Vincenzo Librandi, Oct 08 2009

Keywords

• nonn
• easy

Comments

Numbers m >= 9 such that 8*m - 47 is a square. - Bruce J. Nicholson, Jul 25 2017

Links

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

Crossrefs

Cf. A145018.

Programs

Magma

I:=[9, 12, 16]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Mar 15 2012

Mathematica

Table[n*(n+3)/2+7, {n, 1, 40}] (* or *) LinearRecurrence[{3,-3,1}, {9, 12, 16}, 40] (* Vincenzo Librandi, Mar 15 2012 *)

PARI

for(n=1, 40, print1(n*(n+3)/2+7, ", ")); \\ Vincenzo Librandi, Mar 15 2012

Formula

a(n) = a(n-1) + n = 3*a(n-1) - 3*a(n-2) + a(n-3) = A145018(n+2) + 2.

G.f.: -x*(9 - 15*x + 7*x^2)/(x-1)^3.

E.g.f.: (1/2)*(14 + 4*x + x^2)*exp(x) - 7. - G. C. Greubel, Apr 26 2016

Sum_{n>=1} 1/a(n) = -13/42 + 2*Pi*tanh(sqrt(47)*Pi/2)/sqrt(47). - Amiram Eldar, Dec 13 2022

Extensions

Definition replaced by polynomial from R. J. Mathar, Oct 12 2009