A176916 a(n) = 5^n + 5*n + 1.

2, 11, 36, 141, 646, 3151, 15656, 78161, 390666, 1953171, 9765676, 48828181, 244140686, 1220703191, 6103515696, 30517578201, 152587890706, 762939453211, 3814697265716, 19073486328221, 95367431640726, 476837158203231, 2384185791015736, 11920928955078241, 59604644775390746

Offset: 0

Author

Jonathan Vos Post, Apr 28 2010

Keywords

• nonn
• easy

Examples

			a(3) = 5^3 + 5*3 + 1 = 141.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-11,5).

Crossrefs

Cf. A000351, A008587, A016861, A176691, A176805.

Programs

Mathematica

LinearRecurrence[{7,-11,5},{2,11,36},25] (* Stefano Spezia, Aug 19 2024 *)

PARI

a(n)=5^n+5*n+1 \\ Charles R Greathouse IV, Aug 23 2024

Formula

a(n) = A000351(n) + A008587(n) + 1 = A000351(n) + A016861(n).

From R. J. Mathar, Apr 29 2010: (Start)

a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).

G.f.: ( -2+3*x+19*x^2 ) / ( (5*x-1)*(x-1)^2 ). (End)

E.g.f.: exp(x)*(1 + exp(4*x) + 5*x). - Stefano Spezia, Aug 19 2024

Extensions

First term corrected by several authors, Apr 29 2010

a(22)-a(24) from Stefano Spezia, Aug 19 2024