A250024 - OEIS

%I #28 Apr 04 2025 07:49:35

%S 19,59,99,139,179,219,259,299,339,379,419,459,499,539,579,619,659,699,

%T 739,779,819,859,899,939,979,1019,1059,1099,1139,1179,1219,1259,1299,

%U 1339,1379,1419,1459,1499,1539,1579,1619,1659,1699,1739,1779,1819,1859,1899

%N a(n) = 40*n - 21.

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

%H Karl V. Keller, Jr., <a href="/A250024/b250024.txt">Table of n, a(n) for n = 1..10000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F From _Vincenzo Librandi_, Nov 11 2014: (Start)

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

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

%F From _Elmo R. Oliveira_, Apr 04 2025: (Start)

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

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

%t 40 Range[40] - 21 (* _Alonso del Arte_, Nov 10 2014 *)

%t CoefficientList[Series[(19 + 21 x) / (1 - x)^2, {x, 0, 50}], x] (* _Vincenzo Librandi_, Nov 11 2014 *)

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

%o (Magma) [40*n-21: n in [1..60]]; // _Vincenzo Librandi_, Nov 11 2014

%o (PARI) a(n)=40*n-21 \\ _Charles R Greathouse IV_, May 23 2019

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

%K nonn,easy

%O 1,1

%A _Karl V. Keller, Jr._, Nov 10 2014