A166143 a(n) = 3*n^2 + 3*n - 5.

1, 13, 31, 55, 85, 121, 163, 211, 265, 325, 391, 463, 541, 625, 715, 811, 913, 1021, 1135, 1255, 1381, 1513, 1651, 1795, 1945, 2101, 2263, 2431, 2605, 2785, 2971, 3163, 3361, 3565, 3775, 3991, 4213, 4441, 4675, 4915, 5161, 5413, 5671, 5935, 6205

Offset: 1

Author

Vincenzo Librandi, Oct 08 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Leo Tavares, Illustration: Truncated Point Hexagons
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A003215.

Programs

Magma

[-5+3*n^2+3*n: n in [1..50]];

Mathematica

LinearRecurrence[{3,-3,1}, {1,13,31}, 50] (* G. C. Greubel, Apr 26 2016 *)
Table[3 n^2 + 3 n - 5, {n, 45}] (* or *)
Rest@ CoefficientList[Series[(5 - 16 x + 5 x^2)/(-1 + x)^3, {x, 0, 45}], x] (* Michael De Vlieger, Apr 27 2016 *)

PARI

a(n)=3*n*(n+1)-5 \\ Charles R Greathouse IV, Jan 11 2012

Formula

a(n) = a(n-1)+6*n, a(1)=1.

From G. C. Greubel, Apr 26 2016: (Start)

G.f.: (5 - 16*x + 5*x^2)/(-1 + x)^3.

E.g.f.: (-5 + 6*x + 3*x^2)*exp(x).

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

a(n) = A003215(n) - 6. - Leo Tavares, Jul 05 2021

Sum_{n>=0} 1/a(n) = Pi*tan(sqrt(23/3)*Pi/2)/sqrt(69). - Vaclav Kotesovec, Jul 06 2021

Extensions

New name from Charles R Greathouse IV, Jan 11 2012