A139609 a(n) = 36*n + 9.

9, 45, 81, 117, 153, 189, 225, 261, 297, 333, 369, 405, 441, 477, 513, 549, 585, 621, 657, 693, 729, 765, 801, 837, 873, 909, 945, 981, 1017, 1053, 1089, 1125, 1161, 1197, 1233, 1269, 1305, 1341, 1377, 1413, 1449, 1485, 1521, 1557, 1593, 1629, 1665, 1701

Offset: 0

Author

Omar E. Pol, Apr 27 2008

Keywords

• easy
• nonn

Comments

Numbers of the 9th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A016813, A044102, A057145, A139600, A152994.

Programs

Magma

[9*(4*n + 1): n in [0..60]]; // Vincenzo Librandi, Jul 23 2011

Mathematica

Range[9, 7000, 36] (* Vladimir Joseph Stephan Orlovsky, Jul 23 2011 *)
36*Range[0,50]+9 (* or *) LinearRecurrence[{2,-1},{9,45},50] (* Harvey P. Dale, Jan 04 2018 *)

PARI

a(n)=36*n+9 \\ Charles R Greathouse IV, Oct 05 2011

Formula

a(n) = A057145(n+2,9).

G.f.: 9*(1+3*x)/(x-1)^2. - R. J. Mathar, Jul 28 2016

From Elmo R. Oliveira, Apr 16 2024: (Start)

E.g.f.: 9*exp(x)*(1 + 4*x).

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

a(n) = 9*A016813(n) = A044102(n) + 9 = A152994(n+1) - A152994(n). (End)