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Numbers n such that n^2 = 37*m^2 + 37*m +1.
1

%I #11 Sep 17 2023 17:36:22

%S 1,149,295,21755,43069,3176081,6287779,463686071,917972665,

%T 67694990285,134017721311,9883004895539,19565669338741,

%U 1442851019758409,2856453705734875,210646365879832175,417022675367953009,30752926567435739141,60882454150015404439

%N Numbers n such that n^2 = 37*m^2 + 37*m +1.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,146,0,-1).

%F Define a(1)=1, a(2)=149, a(3)=146*a(1)+a(2), a(4)=146*a(2)+a(1), then a(n)=146*a(n-2)-a(n-4).

%F G.f.: x*(x+1)*(x^2+148*x+1) / ((x^2-12*x-1)*(x^2+12*x-1)). [_Colin Barker_, Mar 06 2013]

%t LinearRecurrence[{0,146,0,-1},{1,149,295,21755},20] (* _Harvey P. Dale_, Sep 17 2023 *)

%Y Cf. A105844 (associated m).

%K nonn,easy

%O 1,2

%A _Pierre CAMI_, Apr 22 2005

%E a(12)-a(19) from _Colin Barker_, Mar 06 2013