A069477 a(n) = 60*n^2 + 180*n + 150.

390, 750, 1230, 1830, 2550, 3390, 4350, 5430, 6630, 7950, 9390, 10950, 12630, 14430, 16350, 18390, 20550, 22830, 25230, 27750, 30390, 33150, 36030, 39030, 42150, 45390, 48750, 52230, 55830, 59550, 63390, 67350, 71430, 75630, 79950, 84390, 88950, 93630, 98430, 103350

Offset: 1

Author

Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Apr 11 2002

Keywords

• nonn
• easy

Comments

First differences of A068236, successive differences of (n+1)^5 - n^5 (A022521).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001844, A022521, A068236, A069477, A069894, A101096.

Programs

Magma

[30*(2*n^2 + 6*n + 5): n in [1..40]]; // Vincenzo Librandi, Nov 23 2011

Mathematica

Table[30 (2 n^2 + 6 n + 5), {n, 1, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)
LinearRecurrence[{3,-3,1},{390,750,1230},40] (* Harvey P. Dale, Apr 06 2012 *)

PARI

a(n)=60*n^2+180*n+150 \\ Charles R Greathouse IV, Nov 23 2011

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=390, a(2)=750, a(3)=1230. - Harvey P. Dale, Apr 06 2012

Sum_{n>=1} 1/a(n) = (Pi/60)*tanh(Pi/2) - 1/25. - Amiram Eldar, Jan 27 2022

From Elmo R. Oliveira, Feb 08 2025: (Start)

G.f.: 30*x*(5*x^2 - 14*x + 13)/(1-x)^3.

E.g.f.: 30*(exp(x)*(2*x^2 + 8*x + 5) - 5).

a(n) = 30*A001844(n+1) = 15*A069894(n+1). (End)