A001534 a(n) = (9*n+1)*(9*n+8).

8, 170, 494, 980, 1628, 2438, 3410, 4544, 5840, 7298, 8918, 10700, 12644, 14750, 17018, 19448, 22040, 24794, 27710, 30788, 34028, 37430, 40994, 44720, 48608, 52658, 56870, 61244, 65780, 70478, 75338, 80360, 85544, 90890, 96398, 102068, 107900, 113894, 120050

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A017173, A017257.

Programs

Mathematica

f[n_]:=Module[{n9=9n},(n9+1)(n9+8)];Array[f,40,0] (* or *) LinearRecurrence[ {3,-3,1},{8,170,494},50] (* Harvey P. Dale, Aug 20 2011 *)

PARI

a(n)=(9*n+1)*(9*n+8) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 162*n + a(n-1) with a(0)=8. - Vincenzo Librandi, Nov 12 2010

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0)=8, a(1)=170, a(2)=494. - Harvey P. Dale, Aug 20 2011

G.f.: -((2*(x*(4*x+73)+4))/(x-1)^3). - Harvey P. Dale, Aug 20 2011

Sum_{n>=0} 1/a(n) = (Psi(8/9)-Psi(1/9))/63 = 0.13700722.. - R. J. Mathar, May 30 2022

Sum_{n>=0} 1/a(n) = cot(Pi/9)*Pi/63. - Amiram Eldar, Sep 10 2022

From Amiram Eldar, Feb 19 2023: (Start)

a(n) = A017173(n)*A017257(n).

Product_{n>=0} (1 - 1/a(n)) = cosec(Pi/9)*cos(sqrt(53)*Pi/18).

Product_{n>=0} (1 + 1/a(n)) = cosec(Pi/9)*cos(sqrt(5)*Pi/6). (End)

E.g.f.: exp(x)*(8 + 81*x*(2 + x)). - Elmo R. Oliveira, Oct 18 2024