OFFSET
0,1
COMMENTS
Cf. comment of Reinhard Zumkeller in A177059: in general, (h*n+h-k)*(h*n+k) = h^2*A002061(n+1) + (h-k)*k - h^2; therefore a(n) = 81*A002061(n+1) - 67. - Bruno Berselli, Aug 24 2010
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 162*n + a(n-1) with n > 0, a(0)=14.
From Vincenzo Librandi, Apr 08 2013: (Start)
G.f.: 2*(7+67*x+7*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
From Amiram Eldar, Feb 19 2023: (Start)
Sum_{n>=0} 1/a(n) = cot(2*Pi/9)*Pi/45.
Product_{n>=0} (1 - 1/a(n)) = cosec(2*Pi/9)*cos(sqrt(29)*Pi/18).
Product_{n>=0} (1 + 1/a(n)) = cosec(2*Pi/9)*cos(sqrt(21)*Pi/18). (End)
E.g.f.: exp(x)*(14 + 81*x*(2 + x)). - Elmo R. Oliveira, Oct 18 2024
MATHEMATICA
CoefficientList[Series[2(7 + 67 x + 7 x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Apr 08 2013 *)
Table[(9*n + 2)*(9*n + 7), {n, 0, 40}] (* Amiram Eldar, Feb 19 2023 *)
LinearRecurrence[{3, -3, 1}, {14, 176, 500}, 50] (* Harvey P. Dale, Jun 10 2023 *)
PROG
(Magma) I:=[14, 176, 500]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Apr 08 2013
(PARI) a(n)=(9*n+2)*(9*n+7) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 31 2010
EXTENSIONS
Edited by N. J. A. Sloane, Jun 22 2010
STATUS
approved