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A105037 a(n) = 22*a(n-2) - a(n-4) + 10, for n > 3, with a(0) = 0, a(1) = 4, a(2) = 6, a(3) = 98.

%I A105037 #18 Jan 05 2024 17:49:26
%S A105037 0,4,6,98,142,2162,3128,47476,68684,1042320,1507930,22883574,33105786,
%T A105037 502396318,726819372,11029835432,15956920408,242153983196,
%U A105037 350325429614,5316357794890,7691202531110,116717717504394,168856130254816
%N A105037 a(n) = 22*a(n-2) - a(n-4) + 10, for n > 3, with a(0) = 0, a(1) = 4, a(2) = 6, a(3) = 98.
%C A105037 It appears this sequence gives all nonnegative m such that 120*m^2 + 120*m + 1 is a square.
%H A105037 G. C. Greubel, <a href="/A105037/b105037.txt">Table of n, a(n) for n = 0..1000</a>
%H A105037 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,22,-22,-1,1).
%F A105037 a(n) = 22*a(n-2) - a(n-4) + 10, for n > 3.
%F A105037 G.f.: 2*x*(2 + x + 2*x^2)/((1-x)*(1-22*x^2+x^4)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
%t A105037 LinearRecurrence[{1,22,-22,-1,1}, {0,4,6,98,142}, 41] (* _G. C. Greubel_, Mar 14 2023 *)
%o A105037 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( 2*x*(2+x+2*x^2)/((1-x)*(1-22*x^2+x^4)) )); // _G. C. Greubel_, Mar 14 2023
%o A105037 (SageMath)
%o A105037 @CachedFunction
%o A105037 def a(n): # a = A105037
%o A105037     if (n<5): return (0,4,6,98,142)[n]
%o A105037     else: return a(n-1) +22*a(n-2) -22*a(n-3) -a(n-4) +a(n-5)
%o A105037 [a(n) for n in range(41)] # _G. C. Greubel_, Mar 14 2023
%Y A105037 Cf. A077421.
%K A105037 nonn,easy
%O A105037 0,2
%A A105037 _Gerald McGarvey_, Apr 03 2005