A165720 Integers of the form k*(k+11)/10.

6, 8, 18, 21, 35, 39, 57, 62, 84, 90, 116, 123, 153, 161, 195, 204, 242, 252, 294, 305, 351, 363, 413, 426, 480, 494, 552, 567, 629, 645, 711, 728, 798, 816, 890, 909, 987, 1007, 1089, 1110, 1196, 1218, 1308, 1331, 1425, 1449, 1547, 1572, 1674, 1700, 1806

Offset

1,1

Comments

Integers of the form k + k*(k+1)/10 = k + A000217(k)/5. For k see A047208, for A000217(k)/5 see A057569. - R. J. Mathar, Sep 25 2009

Are all terms composite numbers?

Yes. They are alternately of the form (h+2)*(5*h-1)/2 and h*(5*h+11)/2, with h>0. - Bruno Berselli, Dec 22 2016

Links

Table of n, a(n) for n=1..51.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

From R. J. Mathar, Sep 25 2009: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).

a(n) = 5*(2*n^2 + 10*n + 3)/16 - 3*(-1)^n*(5 + 2*n)/16.

G.f.: x*(-6 - 2*x + 2*x^2 + x^3) / ((1 + x)^2*(x - 1)^3). (End)

Sum_{n>=1} 1/a(n) = 514/363 - 2*Pi*sqrt(1+2/sqrt(5))/11. - Amiram Eldar, Jul 26 2024

Mathematica

Select[k = Range[0, 130]; k (k + 11)/10, IntegerQ] (* Bruno Berselli, Dec 22 2016 *)

Crossrefs

Cf. A000217, A047208, A057569, A165717, A165718, A165719, A279895.

Sequence in context: A315942 A315943 A315944 * A315945 A086913 A108341

Adjacent sequences: A165717 A165718 A165719 * A165721 A165722 A165723

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 24 2009

Extensions

Definition simplified by R. J. Mathar, Sep 25 2009

Corrected A-number in my comment - R. J. Mathar, Oct 30 2009

Status

approved