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%I #27 Sep 08 2022 08:46:08
%S 1,5,9,37,113,261,505,869,1377,2053,2921,4005,5329,6917,8793,10981,
%T 13505,16389,19657,23333,27441,32005,37049,42597,48673,55301,62505,
%U 70309,78737,87813,97561,108005,119169,131077,143753,157221,171505,186629,202617,219493
%N 4*n^3 + 5.
%C Squares in the sequence: 1, 9, 5329, for n = -1, 1, 11 respectively. No other square for n < 9*10^9.
%H Vincenzo Librandi, <a href="/A243762/b243762.txt">Table of n, a(n) for n = -1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: (-1 + 9*x - 17*x^2 + 35*x^3 - 2*x^4)/(1 - x)^4.
%F a(n) = 4*A000578(n-1)+5 = 4*A001093(n)+1.
%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3.
%F a(n) = A033430(n-1) + 5. - _Wesley Ivan Hurt_, Jun 10 2014
%p A243762:=n->4*n^3 + 5; seq(A243762(n), n=-1..40); # _Wesley Ivan Hurt_, Jun 10 2014
%t Table[4 n^3 + 5, {n, -1, 50}] (* or *) CoefficientList[Series[(-1 + 9 x - 17 x^2 + 35 x^3 - 2 x^4)/(1 - x)^4, {x, 0, 40}], x]
%o (Magma) [4*n^3+5: n in [-1..40]]; /* or */ I:=[1,5,9,37]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]
%Y Cf. A000578, A033430.
%K nonn,easy
%O -1,2
%A _Vincenzo Librandi_, Jun 10 2014
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