A159007 Numbers k such that k == 32 or 41 (mod 73).

32, 41, 105, 114, 178, 187, 251, 260, 324, 333, 397, 406, 470, 479, 543, 552, 616, 625, 689, 698, 762, 771, 835, 844, 908, 917, 981, 990, 1054, 1063, 1127, 1136, 1200, 1209, 1273, 1282, 1346, 1355, 1419, 1428, 1492, 1501, 1565, 1574, 1638, 1647, 1711, 1720

Offset: 1

Author

Vincenzo Librandi, Jun 30 2009

Keywords

• nonn
• easy

Comments

Also, numbers k such that k^2 == 2 (mod 73).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Magma

I:=[32, 41, 105]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Mar 02 2012

Mathematica

LinearRecurrence[{1,1,-1},{32,41,105},60] (* Harvey P. Dale, Aug 09 2016 *)

PARI

for(n=1, 50, print1((73+55*(-1)^(n-1)+146*(n-1))/4", ")); \\ Vincenzo Librandi, Mar 02 2012

Formula

a(n) = a(n-1) + a(n-2) - a(n-3) with a(1)=32, a(2)=41, a(3)=105.

a(n) = (73 + 55*(-1)^(n-1) + 146*(n-1))/4.

G.f.: x*(32 + 9*x + 32*x^2)/((1+x)*(x-1)^2). - R. J. Mathar, Jul 18 2009

Extensions

Sign of k in the definition clarified by R. J. Mathar, Jul 18 2009

New name from Charles R Greathouse IV, Jan 11 2012