|
%I #20 Sep 08 2022 08:45:54
%S 1,91,131,401,481,931,1051,1681,1841,2651,2851,3841,4081,5251,5531,
%T 6881,7201,8731,9091,10801,11201,13091,13531,15601,16081,18331,18851,
%U 21281,21841,24451,25051,27841,28481,31451,32131,35281,36001,39331
%N Positive integers of the form (10*m^2+1)/11.
%C Here m=(11*(2*n-1)+7*(-1)^n)/4 for n>0.
%H B. Berselli, <a href="/A179338/b179338.txt">Table of n, a(n) for n = 1..10000</a>.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F a(n) = (110*n*(n-1)+35*(2*n-1)*(-1)^n+39)/4.
%F G.f.: x*(1+90*x+38*x^2+90*x^3+1*x^4)/((1+x)^2*(1-x)^3).
%F a(n) = a(-n+1) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).
%t Select[(10Range[300]^2+1)/11,IntegerQ] (* or *) LinearRecurrence[ {1,2,-2,-1,1},{1,91,131,401,481},50] (* _Harvey P. Dale_, Jul 10 2014 *)
%o (PARI) isok(n) = (((11*n-1) % 10 == 0) && issquare((11*n-1)/10)) \\ _Michel Marcus_, Jun 07 2013
%o (Magma) [(110*n*(n-1)+35*(2*n-1)*(-1)^n+39)/4: n in [1..50]]; // _Vincenzo Librandi_, Jul 10 2014
%Y Cf. A113338, A179088, A179337, A179339, A179370.
%K nonn,easy
%O 1,2
%A _Bruno Berselli_, Jul 11 2010
|
