A185019 a(n) = n*(14*n-3).

0, 11, 50, 117, 212, 335, 486, 665, 872, 1107, 1370, 1661, 1980, 2327, 2702, 3105, 3536, 3995, 4482, 4997, 5540, 6111, 6710, 7337, 7992, 8675, 9386, 10125, 10892, 11687, 12510, 13361, 14240, 15147, 16082, 17045, 18036, 19055, 20102, 21177, 22280, 23411, 24570

Offset: 0

Author

Bruno Berselli, Oct 14 2011 - based on remarks and sequences by Omar E. Pol

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Bruno Berselli, Illustration of initial terms: An origin of A185019.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A013656, A033429, A049452, A049453, A147296, A195025.

Cf. A000384, A195023, A195024, A135703.

Cf. A195020 (vertices of the numerical spiral in link).

Programs

Magma

[n*(14*n-3): n in [0..42]];

Magma

I:=[0,11,50]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Aug 18 2013

Mathematica

CoefficientList[Series[x (11 + 17 x)/(1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)

PARI

for(n=0, 42, print1(n*(14*n-3)", "));

Formula

G.f.: x*(11+17*x)/(1-x)^3.

a(n) = A195025(-n).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. - Wesley Ivan Hurt, Dec 18 2020

From Elmo R. Oliveira, Dec 30 2024: (Start)

E.g.f.: exp(x)*x*(11 + 14*x).

a(n) = n + A195023(n). (End)