A139607 a(n) = 21*n + 7.

7, 28, 49, 70, 91, 112, 133, 154, 175, 196, 217, 238, 259, 280, 301, 322, 343, 364, 385, 406, 427, 448, 469, 490, 511, 532, 553, 574, 595, 616, 637, 658, 679, 700, 721, 742, 763, 784, 805, 826, 847, 868, 889, 910, 931, 952, 973, 994

Offset: 0

Author

Omar E. Pol, Apr 27 2008

Keywords

• easy
• nonn

Comments

Numbers of the 7th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.

7th transversal numbers (or 7-transversal numbers): (A000217(7)-7)*n + 7.

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. A000217, A008603, A016777, A057145, A139600, A152744.

Programs

Magma

[21*n+7: n in [0..60]]; // Vincenzo Librandi, Jul 23 2011

Mathematica

Range[7, 1500, 21] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
21*Range[0,50]+7 (* or *) LinearRecurrence[{2,-1},{7,28},50] (* Harvey P. Dale, Feb 23 2020 *)

PARI

a(n)=21*n+7 \\ Charles R Greathouse IV, Oct 05 2011

Formula

a(n) = A057145(n+2,7).

G.f.: 7*(1+2*x)/(x-1)^2. - R. J. Mathar, Jul 28 2016

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

E.g.f.: 7*exp(x)*(1 + 3*x).

a(n) = 7*A016777(n) = A008603(n) + 7 = A152744(n+1) - A152744(n).

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