A139606 a(n) = 15*n + 6.

6, 21, 36, 51, 66, 81, 96, 111, 126, 141, 156, 171, 186, 201, 216, 231, 246, 261, 276, 291, 306, 321, 336, 351, 366, 381, 396, 411, 426, 441, 456, 471, 486, 501, 516, 531, 546, 561, 576, 591, 606, 621, 636, 651, 666, 681, 696, 711, 726, 741, 756, 771, 786

Offset: 0

Author

Omar E. Pol, Apr 27 2008

Keywords

• easy
• nonn

Comments

Numbers of the 6th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.

6th transversal numbers (or 6-transversal numbers): (A000217(6)-6)*n + 6.

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189. - From N. J. A. Sloane, Dec 01 2012

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. A067076, A144562, A153238.

Cf. A000217, A008597, A016873, A057145, A139600.

Programs

Magma

[15*n+6 : n in [0..60]]; // Vincenzo Librandi, Oct 06 2011

Mathematica

Range[6, 1000, 15] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
15*Range[0,60]+6 (* or *) LinearRecurrence[{2,-1},{6,21},60] (* Harvey P. Dale, Aug 09 2019 *)

PARI

a(n)=15*n+6 \\ Charles R Greathouse IV, Oct 05 2011

Formula

a(n) = A057145(n+2,6).

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

From Elmo R. Oliveira, Apr 12 2024: (Start)

E.g.f.: 3*exp(x)*(2 + 5*x).

a(n) = 3*A016873(n) = A008597(n) + 6.

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