A152161 a(n) = 100*n^2 + 100*n + 21.

21, 221, 621, 1221, 2021, 3021, 4221, 5621, 7221, 9021, 11021, 13221, 15621, 18221, 21021, 24021, 27221, 30621, 34221, 38021, 42021, 46221, 50621, 55221, 60021, 65021, 70221, 75621, 81221, 87021, 93021, 99221, 105621, 112221, 119021, 126021, 133221, 140621, 148221

Offset: 0

Author

Paul Curtz, Nov 27 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001622, A017305, A017353, A061037.

Programs

Magma

[(10*n+3)*(10*n+7): n in [0..40]]; // Vincenzo Librandi, Jul 28 2011

Mathematica

Table[100*n^2 + 100*n + 21, {n,0,50}] (* G. C. Greubel, Sep 20 2018 *)
LinearRecurrence[{3,-3,1},{21,221,621},40] (* Harvey P. Dale, Dec 06 2018 *)

PARI

a(n)=100*n*(n+1)+21 \\ Charles R Greathouse IV, Jul 28 2011

Formula

a(n) = A017305(n)*A017353(n) = A061037(10*n+3).

From Amiram Eldar, Feb 20 2023: (Start)

Sum_{n>=0} 1/a(n) = sqrt(5-2*sqrt(5))*Pi/40.

Sum_{n>=0} (-1)^n/a(n) = (sqrt(10-2*sqrt(5))*log(cot(Pi/20)) + sqrt(10+2*sqrt(5))*log(tan(3*Pi/20)))/40.

Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/10)/phi, where phi is the golden ratio (A001622).

Product_{n>=0} (1 + 1/a(n)) = 2*cos(sqrt(3)*Pi/10)/phi. (End)

From Elmo R. Oliveira, Nov 27 2024: (Start)

G.f.: (21 + 158*x + 21*x^2)/(1-x)^3.

E.g.f.: (21 + 200*x + 100*x^2)*exp(x).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 3. (End)