A153127 a(n) = (2*n + 1)*(5*n + 6).

6, 33, 80, 147, 234, 341, 468, 615, 782, 969, 1176, 1403, 1650, 1917, 2204, 2511, 2838, 3185, 3552, 3939, 4346, 4773, 5220, 5687, 6174, 6681, 7208, 7755, 8322, 8909, 9516, 10143, 10790, 11457, 12144, 12851, 13578, 14325, 15092, 15879, 16686, 17513

Offset: 0

Author

Reinhard Zumkeller, Dec 20 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000566, A001622, A005408, A016861, A019952, A033571, A153126.

Programs

Mathematica

Table[(2n+1)(5n+6),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{6,33,80},50] (* Harvey P. Dale, Jun 07 2021 *)

PARI

a(n)=(2*n+1)*(5*n+6) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = A153126(2*n+1) = A000566(2*(n+1)) - 1.

a(n) = a(n-1) + 20*n + 7 (with a(0)=6). - Vincenzo Librandi, Dec 27 2010

G.f.: (-6-15*x+x^2)/(-1+x)^3 - Harvey P. Dale, Jun 07 2021

Sum_{n>=0} 1/a(n) = 5/7 - sqrt(1+2/sqrt(5))*Pi/14 - sqrt(5)*log(phi)/14 - 5*log(5)/28 + 2*log(2)/7, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 23 2022

From Elmo R. Oliveira, Oct 27 2024: (Start)

E.g.f.: exp(x)*(6 + 27*x + 10*x^2).

a(n) = A005408(n)*A016861(n+1).

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