A001545 a(n) = (5*n+1)*(5*n+4).

4, 54, 154, 304, 504, 754, 1054, 1404, 1804, 2254, 2754, 3304, 3904, 4554, 5254, 6004, 6804, 7654, 8554, 9504, 10504, 11554, 12654, 13804, 15004, 16254, 17554, 18904, 20304, 21754, 23254, 24804, 26404, 28054, 29754, 31504, 33304, 35154, 37054, 39004, 41004, 43054

Offset

0,1

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 50*A000217(n) + 4.

a(n) = 50*n + a(n-1) with a(0)=4. - Vincenzo Librandi, Jan 20 2011

From Amiram Eldar, Jan 23 2022: (Start)

Sum_{n>=0} 1/a(n) = sqrt(1 + 2/sqrt(5))*Pi/15 = 0.2882687....

Sum_{n>=0} (-1)^n/a(n) = 2*log(phi)/(3*sqrt(5)) + 2*log(2)/15, where phi is the golden ratio (A001622).

Product_{n>=0} (1 - 1/a(n)) = sqrt(2 + 2/sqrt(5)) * cos(sqrt(13)*Pi/10).

Product_{n>=0} (1 + 1/a(n)) = sqrt(2 + 2/sqrt(5)) * cos(Pi/(2*sqrt(5))).

Product_{n>=0} (1 + 2/a(n)) = phi. (End)

G.f.: 2*(2+21*x+2*x^2)/(1-x)^3. - R. J. Mathar, May 30 2022

Sum_{n>=0} 1/a(n) = (Psi(4/5) - Psi(1/5))/15. See A200135, A200138. - R. J. Mathar, May 30 2022

From Elmo R. Oliveira, Oct 23 2024: (Start)

E.g.f.: exp(x)*(4 + 25*x*(2 + x)).

a(n) = A016861(n)*A016897(n).

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

Mathematica

Table[(5n+1)(5n+4), {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {4, 54, 154}, 60] (* Harvey P. Dale, Mar 17 2019 *)

Prog

(PARI) a(n)=(5*n+1)*(5*n+4) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217, A001622, A016861, A016897, A177059, A200135, A200138.

Sequence in context: A362050 A095210 A156469 * A208954 A269507 A302942

Adjacent sequences: A001542 A001543 A001544 * A001546 A001547 A001548

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved