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

%I A159007 #20 Sep 08 2022 08:45:43
%S A159007 32,41,105,114,178,187,251,260,324,333,397,406,470,479,543,552,616,
%T A159007 625,689,698,762,771,835,844,908,917,981,990,1054,1063,1127,1136,1200,
%U A159007 1209,1273,1282,1346,1355,1419,1428,1492,1501,1565,1574,1638,1647,1711,1720
%N A159007 Numbers k such that k == 32 or 41 (mod 73).
%C A159007 Also, numbers k such that k^2 == 2 (mod 73).
%H A159007 Vincenzo Librandi, <a href="/A159007/b159007.txt">Table of n, a(n) for n = 1..1000</a>
%H A159007 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A159007 a(n) = a(n-1) + a(n-2) - a(n-3) with a(1)=32, a(2)=41, a(3)=105.
%F A159007 a(n) = (73 + 55*(-1)^(n-1) + 146*(n-1))/4.
%F A159007 G.f.: x*(32 + 9*x + 32*x^2)/((1+x)*(x-1)^2). - _R. J. Mathar_, Jul 18 2009
%t A159007 LinearRecurrence[{1,1,-1},{32,41,105},60] (* _Harvey P. Dale_, Aug 09 2016 *)
%o A159007 (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
%o A159007 (PARI) for(n=1, 50, print1((73+55*(-1)^(n-1)+146*(n-1))/4", ")); \\ _Vincenzo Librandi_, Mar 02 2012
%K A159007 nonn,easy
%O A159007 1,1
%A A159007 _Vincenzo Librandi_, Jun 30 2009
%E A159007 Sign of k in the definition clarified by _R. J. Mathar_, Jul 18 2009
%E A159007 New name from _Charles R Greathouse IV_, Jan 11 2012