OFFSET
0,1
COMMENTS
Cf. Zumkeller's contribution in A177059: in general, (h*n+h-k)*(h*n+k) = h^2*A002061(n+1) + (h-k)*k - h^2, therefore a(n) = 49*A002061(n+1) - 37. - Bruno Berselli, Aug 24 2010
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 98*n + a(n-1) with n > 0, a(0)=12.
From Harvey P. Dale, Oct 09 2011: (Start)
a(0)=12, a(1)=110, a(2)=306, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: -((2*(x+6)*(6*x+1))/(x-1)^3). (End)
From Amiram Eldar, Feb 19 2023: (Start)
Sum_{n>=0} 1/a(n) = tan(Pi/14)*Pi/7.
Product_{n>=0} (1 - 1/a(n)) = sec(Pi/14)*cos(sqrt(5)*Pi/14).
Product_{n>=0} (1 + 1/a(n)) = sec(Pi/14)*cosh(sqrt(3)*Pi/14). (End)
From Elmo R. Oliveira, Oct 27 2024: (Start)
E.g.f.: exp(x)*(12 + 49*x*(2 + x)).
a(n) = 2*A061792(n). (End)
MATHEMATICA
Table[(7n+3)(7n+4), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {12, 110, 306}, 40] (* Harvey P. Dale, Oct 09 2011 *)
PROG
(PARI) a(n)=2*binomial(7*n+4, 2) \\ Charles R Greathouse IV, Jan 11 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 31 2010
EXTENSIONS
Edited by N. J. A. Sloane, Jun 22 2010
STATUS
approved