A067705 a(n) = 11*n^2 + 22*n.

33, 88, 165, 264, 385, 528, 693, 880, 1089, 1320, 1573, 1848, 2145, 2464, 2805, 3168, 3553, 3960, 4389, 4840, 5313, 5808, 6325, 6864, 7425, 8008, 8613, 9240, 9889, 10560, 11253, 11968, 12705, 13464, 14245, 15048, 15873, 16720, 17589, 18480, 19393, 20328, 21285

Offset: 1

Author

Robert G. Wilson v, Feb 05 2002

Keywords

• nonn
• easy

Comments

Numbers k such that 11*(11 + k) is a perfect square.

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. A067724, A067725, A067726, A067727, A067728 (if 11 is replaced by 3, 5, 6, 7, 8 respectively), A067707 (12).

Cf. A005563.

Programs

Magma

[11*n*(n+2): n in [1..50]]; // Vincenzo Librandi, Jul 07 2012

Mathematica

Select[ Range[20000], IntegerQ[ Sqrt[ 11(11 + # )]] & ]
CoefficientList[Series[11 (3 - x)/(1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)

PARI

a(n)=11*n*(n+2) \\ Charles R Greathouse IV, Dec 07 2011

Formula

From Vincenzo Librandi, Jul 07 2012: (Start)

G.f.: 11*x*(3-x)/(1-x)^3.

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

From Elmo R. Oliveira, Jan 28 2025: (Start)

E.g.f.: 11*exp(x)*x*(3 + x).

a(n) = 11*A005563(n). (End)