A250024 a(n) = 40*n - 21.

19, 59, 99, 139, 179, 219, 259, 299, 339, 379, 419, 459, 499, 539, 579, 619, 659, 699, 739, 779, 819, 859, 899, 939, 979, 1019, 1059, 1099, 1139, 1179, 1219, 1259, 1299, 1339, 1379, 1419, 1459, 1499, 1539, 1579, 1619, 1659, 1699, 1739, 1779, 1819, 1859, 1899

Offset: 1

Author

Karl V. Keller, Jr., Nov 10 2014

Keywords

• nonn
• easy

Comments

This is the sequence of numbers congruent to 19 mod 40.

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A017377 (10*n+9), A142190 (prime terms).

Programs

Magma

[40*n-21: n in [1..60]]; // Vincenzo Librandi, Nov 11 2014

Mathematica

40 Range[40] - 21 (* Alonso del Arte, Nov 10 2014 *)
CoefficientList[Series[(19 + 21 x) / (1 - x)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Nov 11 2014 *)

PARI

a(n)=40*n-21 \\ Charles R Greathouse IV, May 23 2019

Python

for n in range(1,101): print(40*n-21,end=",")

Formula

From Vincenzo Librandi, Nov 11 2014: (Start)

G.f.: x*(19+21*x)/(1-x)^2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

From Elmo R. Oliveira, Apr 04 2025: (Start)

E.g.f.: 21 + exp(x)*(40*x - 21).

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