cp's OEIS Frontend

A222182 Numbers m such that 2*m + 11 is a square.

%I A222182 #26 Nov 17 2024 18:56:19
%S A222182 -5,-1,7,19,35,55,79,107,139,175,215,259,307,359,415,475,539,607,679,
%T A222182 755,835,919,1007,1099,1195,1295,1399,1507,1619,1735,1855,1979,2107,
%U A222182 2239,2375,2515,2659,2807,2959,3115,3275,3439,3607,3779,3955,4135,4319,4507,4699
%N A222182 Numbers m such that 2*m + 11 is a square.
%C A222182 Except the first term, main diagonal of A155546. - _Vincenzo Librandi_, Mar 04 2013
%H A222182 Bruno Berselli, <a href="/A222182/b222182.txt">Table of n, a(n) for n = 1..1000</a>
%H A222182 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A222182 G.f.: -x*(5 - 14*x + 5*x^2)/(1-x)^3.
%F A222182 a(n) = a(-n+1) = 2*n^2 - 2*n - 5.
%F A222182 a(n) = A046092(n-1) - 5.
%F A222182 Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(11)*Pi/2)/(2*sqrt(11)). - _Amiram Eldar_, Dec 23 2022
%F A222182 From _Elmo R. Oliveira_, Nov 17 2024: (Start)
%F A222182 E.g.f.: exp(x)*(2*x^2 - 5) + 5.
%F A222182 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A222182 Table[2 n^2 - 2 n - 5, {n, 50}]
%o A222182 (Magma) [m: m in [-5..5000] | IsSquare(2*m+11)];
%o A222182 (Maxima) makelist(coeff(taylor(-(5-14*x+5*x^2)/(1-x)^3, x, 0, n), x, n), n, 0, 50);
%o A222182 (Magma) I:=[-5,-1,7]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Mar 04 2013
%o A222182 (PARI) a(n)=2*n^2-2*n-5 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A222182 Cf. numbers n such that 2*n + 2*k + 1 is a square: A046092 (k=0), A142463 (k=1), A090288 (k=2), A059993 (k=3), A139570 (k=4), this sequence (k=5), A181510 (k=6).
%Y A222182 Cf. A005408 (square roots of 2*a(n)+11), A155546.
%Y A222182 After a(2), subsequence of A168489.
%K A222182 sign,easy
%O A222182 1,1
%A A222182 _Bruno Berselli_, Mar 01 2013