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 A219392 Numbers k such that 22*k+1 is a square. 3
 0, 20, 24, 84, 92, 192, 204, 344, 360, 540, 560, 780, 804, 1064, 1092, 1392, 1424, 1764, 1800, 2180, 2220, 2640, 2684, 3144, 3192, 3692, 3744, 4284, 4340, 4920, 4980, 5600, 5664, 6324, 6392, 7092, 7164, 7904, 7980, 8760, 8840, 9660, 9744, 10604, 10692 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, numbers of the form m*(22*m+2), where m = 0,-1,1,-2,2,-3,3,... Also, integer values of 2*h*(h+1)/11. LINKS Bruno Berselli, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1). FORMULA G.f.: 4*x^2*(5 + x + 5*x^2)/((1 + x)^2*(1 - x)^3). a(n) = a(-n+1) = (22*n*(n-1) + 9*(-1)^n*(2*n - 1) + 1)/4 + 2. Sum_{n>=2} 1/a(n) = 11/2 - cot(Pi/11)*Pi/2. - Amiram Eldar, Mar 16 2022 MAPLE A219392:=proc(q) local n; for n from 1 to q do if type(sqrt(22*n+1), integer) then print(n); fi; od; end: A219392(1000); # Paolo P. Lava, Feb 19 2013 MATHEMATICA Select[Range[0, 11000], IntegerQ[Sqrt[22 # + 1]] &] CoefficientList[Series[4 x (5 + x + 5 x^2)/((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2013 *) PROG (Magma) [n: n in [0..11000] | IsSquare(22*n+1)]; (Magma) I:=[0, 20, 24, 84, 92]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Aug 18 2013 CROSSREFS Cf. similar sequences listed in A219257. Sequence in context: A347190 A263016 A107302 * A193572 A167323 A112819 Adjacent sequences: A219389 A219390 A219391 * A219393 A219394 A219395 KEYWORD nonn,easy AUTHOR Bruno Berselli, Nov 22 2012 STATUS approved

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Last modified June 2 14:40 EDT 2023. Contains 363097 sequences. (Running on oeis4.)