A214675 a(n) = 9*n^2 - 13*n + 5.

1, 15, 47, 97, 165, 251, 355, 477, 617, 775, 951, 1145, 1357, 1587, 1835, 2101, 2385, 2687, 3007, 3345, 3701, 4075, 4467, 4877, 5305, 5751, 6215, 6697, 7197, 7715, 8251, 8805, 9377, 9967, 10575, 11201, 11845, 12507, 13187, 13885, 14601, 15335, 16087

Offset: 1

Author

Reinhard Zumkeller, Jul 25 2012

Keywords

• nonn
• easy

Comments

Central terms of triangle A214661.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000567, A001106, A214661.

Cf. A220083 for a list of numbers of the form n*P(s,n)-(n-1)*P(s,n-1), where P(s,n) is the n-th polygonal number with s sides.

Programs

Haskell

a214675 n = (9 * n - 13) * n + 5

Magma

[(3*n-2)^2-(n-1): n in [1..50]]; // G. C. Greubel, Mar 08 2024

Mathematica

Table[9n^2-13n+5,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,15,47}, 50] (* Harvey P. Dale, Nov 09 2019 *)

PARI

a(n)=9*n^2-13*n+5 \\ Charles R Greathouse IV, Oct 07 2015

SageMath

[(3*n-2)^2-(n-1) for n in range(1,51)] # G. C. Greubel, Mar 08 2024

Formula

G.f.: x*(1+12*x+5*x^2)/(1-x)^3. - Bruno Berselli, Dec 10 2012

a(n) = n*A000567(n)-(n-1)*A000567(n-1). - Bruno Berselli, Dec 10 2012

E.g.f.: -5 + (5 - 4*x + 9*x^2)*exp(x). - G. C. Greubel, Mar 08 2024