A154576 a(n) = 2*n^2 + 14*n + 5.

21, 41, 65, 93, 125, 161, 201, 245, 293, 345, 401, 461, 525, 593, 665, 741, 821, 905, 993, 1085, 1181, 1281, 1385, 1493, 1605, 1721, 1841, 1965, 2093, 2225, 2361, 2501, 2645, 2793, 2945, 3101, 3261, 3425, 3593, 3765, 3941, 4121, 4305, 4493, 4685, 4881

Offset: 1

Author

Vincenzo Librandi, Jan 12 2009

Keywords

• nonn
• easy

Comments

Seventh diagonal in A144562.

2*a(n) + 39 is a 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. A144562, A154577.

Programs

Magma

I:=[21, 41, 65]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 22 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {21, 41, 65}, 50] (* Vincenzo Librandi, Feb 22 2012 *)

PARI

for(n=1, 40, print1(2*n^2 + 14*n + 5", ")); \\ Vincenzo Librandi, Feb 22 2012

Formula

G.f.: x*(3-x)*(7-5*x)/(1-x)^3. - Bruno Berselli, Dec 07 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 22 2012

Sum_{n>=1} 1/a(n) = 124/1995 + tan(sqrt(39)*Pi/2)*Pi/(2*sqrt(39)). - Amiram Eldar, Feb 25 2023