A008603 Multiples of 21.

0, 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029, 1050, 1071, 1092

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Sum of the numbers from 3*(n-1) to 3*(n+1). - Bruno Berselli, Oct 25 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences.
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 333.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008585, A008589, A008601, A008602.

Programs

Magma

A008603:= func< n | 21*n >; // G. C. Greubel, Apr 16 2025

Mathematica

Range[0, 1500, 21] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
CoefficientList[Series[21 x/(1-x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Jun 10 2013 *)

PARI

a(n)=21*n \\ Charles R Greathouse IV, Oct 07 2015

Python

def A008603(n): return 21*n # G. C. Greubel, Apr 16 2025

Formula

G.f.: 21*x/(1-x)^2. - Vincenzo Librandi, Jun 10 2013

From Elmo R. Oliveira, Apr 08 2025: (Start)

E.g.f.: 21*x*exp(x).

a(n) = A008585(A008589(n)) = A008589(A008585(n)). (End)