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) = 49*A002061(n+1) - 39. - Bruno Berselli, Aug 24 2010
LINKS
FORMULA
a(n) = 98*n + a(n-1) with a(0) = 10.
From Amiram Eldar, Feb 19 2023: (Start)
Sum_{n>=0} 1/a(n) = tan(3*Pi/14)*Pi/21.
Product_{n>=0} (1 - 1/a(n)) = sec(3*Pi/14)*cos(sqrt(13)*Pi/14).
Product_{n>=0} (1 + 1/a(n)) = sec(3*Pi/14)*cos(sqrt(5)*Pi/14). (End)
From Elmo R. Oliveira, Oct 24 2024: (Start)
G.f.: 2*(5 + 39*x + 5*x^2)/(1 - x)^3.
E.g.f.: exp(x)*(10 + 49*x*(2 + x)).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
EXAMPLE
For n=1, a(1) = 98 + 10 = 108.
For n=2, a(2) = 98*2 + 108 = 304.
For n=3, a(3) = 98*3 + 304 = 598.
MATHEMATICA
a[n_] := (7*n + 2)*(7*n + 5); Array[a, 40, 0] (* Amiram Eldar, Feb 19 2023 *)
PROG
(PARI) a(n)=49*n*(n+1)+10 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Vincenzo Librandi, May 31 2010
STATUS
approved