A124388 a(n) = 27*n + 18.

18, 45, 72, 99, 126, 153, 180, 207, 234, 261, 288, 315, 342, 369, 396, 423, 450, 477, 504, 531, 558, 585, 612, 639, 666, 693, 720, 747, 774, 801, 828, 855, 882, 909, 936, 963, 990, 1017, 1044, 1071, 1098, 1125, 1152, 1179, 1206, 1233, 1260, 1287, 1314, 1341, 1368

Offset: 0

Author

Reinhard Zumkeller, Oct 30 2006

Keywords

• nonn
• easy

Comments

Second differences of dodecahedral numbers (A006566).

Also, first differences of dodecahedral gnomic numbers (A093485); a(n+1) - a(n) = 27.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A006566, A016789, A093485.

Programs

Magma

[27*n+18: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011

Mathematica

Range[18, 7000, 27] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)

PARI

for(n=0, 1e2, print1(27*n+18, ", ")) \\ Felix Fröhlich, Jul 07 2014

Formula

a(n) = 9*A016789(n).

G.f.: 9*(2 + x)/(x-1)^2. - R. J. Mathar, Jul 02 2011

From Elmo R. Oliveira, Dec 08 2024: (Start)

E.g.f.: 9*exp(x)*(2 + 3*x).

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

Sum_{n>=0} (-1)^n/a(n) = (Pi/sqrt(3) - log(2))/27. - Amiram Eldar, May 11 2025