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

0,2

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).

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)

Mathematica

Range[0, 1500, 21] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
(* Alternative: *)
CoefficientList[Series[21 x/(1-x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Jun 10 2013 *)
(* Alternative: *)
NestList[21+#&, 0, 60] (* Harvey P. Dale, Jul 05 2026 *)
(* Alternative: *)
LinearRecurrence[{2, -1}, {0, 21}, 60] (* Harvey P. Dale, Jul 05 2026 *)

Prog

(PARI) a(n)=21*n \\ Charles R Greathouse IV, Oct 07 2015
(Magma) A008603:= func< n | 21*n >; // G. C. Greubel, Apr 16 2025
(Python) def A008603(n): return 21*n # G. C. Greubel, Apr 16 2025

Crossrefs

Cf. A008585, A008589, A008601, A008602.

Sequence in context: A037978 A089059 A114384 * A235497 A086794 A001682

Adjacent sequences: A008600 A008601 A008602 * A008604 A008605 A008606

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved