A215146 a(n) = 21*n + 1.

1, 22, 43, 64, 85, 106, 127, 148, 169, 190, 211, 232, 253, 274, 295, 316, 337, 358, 379, 400, 421, 442, 463, 484, 505, 526, 547, 568, 589, 610, 631, 652, 673, 694, 715, 736, 757, 778, 799, 820, 841, 862, 883, 904, 925, 946, 967, 988, 1009, 1030, 1051, 1072

Offset: 0

Author

Jeremy Gardiner, Aug 04 2012

Keywords

• nonn
• easy

Links

• Jeremy Gardiner, Table of n, a(n) for n = 0..999
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A016777, A016993, A124198, A161709.

Programs

Magma

I:=[1,22]; [n le 2 select I[n] else 2*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Apr 19 2018

Mathematica

Range[1, 1000, 21]
LinearRecurrence[{2,-1}, {1,22}, 50] (* G. C. Greubel, Apr 19 2018 *)

PARI

for(n=0, 50, print1(21*n + 1, ", ")) \\ G. C. Greubel, Apr 19 2018

Formula

From G. C. Greubel, Apr 19 2018: (Start)

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

G.f.: (1+20*x)/(1-x)^2.

E.g.f.: (21*x + 1)*exp(x). (End)

a(n) = A016993(3*n) = A016777(7*n). - Elmo R. Oliveira, Apr 12 2025