A177060 a(n) = (7*n+2)*(7*n+5) = 49*n^2 + 49*n + 10.

10, 108, 304, 598, 990, 1480, 2068, 2754, 3538, 4420, 5400, 6478, 7654, 8928, 10300, 11770, 13338, 15004, 16768, 18630, 20590, 22648, 24804, 27058, 29410, 31860, 34408, 37054, 39798, 42640, 45580, 48618, 51754, 54988, 58320, 61750, 65278, 68904, 72628, 76450

Offset: 0

Author

Vincenzo Librandi, May 31 2010

Keywords

• nonn
• easy

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

Examples

			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.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A002061, A017005, A017041, A177059.

Programs

Mathematica

a[n_] := (7*n + 2)*(7*n + 5); Array[a, 40, 0] (* Amiram Eldar, Feb 19 2023 *)

PARI

a(n)=49*n*(n+1)+10 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 98*n + a(n-1) with a(0) = 10.

From Amiram Eldar, Feb 19 2023: (Start)

a(n) = A017005(n)*A017041(n).

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)