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%I #16 Nov 16 2019 13:22:14
%S -1,3,7,15,23,35,47,63,79,99,119,143,167,195,223,255,287,323,359,399,
%T 439,483,527,575,623,675,727,783,839,899,959,1023,1087,1155,1223,1295,
%U 1367,1443,1519,1599,1679,1763,1847,1935,2023,2115,2207,2303,2399,2499
%N Largest odd number strictly less than a square.
%C The terms are the negatives of A141354 and therefore have the same generating function except the sign.
%H Colin Barker, <a href="/A181106/b181106.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 (2,0,-2,1).
%F a(n) = n^2 - 2^(n mod 2) = -A141354(n-1).
%F From _Colin Barker_, Jun 27 2015: (Start)
%F a(n) = n^2 - 1 for n even; a(n) = n^2 - 2 for n odd.
%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F G.f.: x*(x^3-x^2-5*x+1) / ((x-1)^3*(x+1)).
%F (End)
%t Table[n^2-2^Mod[n,2],{n,50}] (* _Ray Chandler_, Dec 05 2011*)
%t LinearRecurrence[{2,0,-2,1},{-1,3,7,15},50] (* _Harvey P. Dale_, Nov 16 2019 *)
%o (PARI) Vec(x*(x^3-x^2-5*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ _Colin Barker_, Jun 27 2015
%Y Equals minus A141354.
%Y Cf. A120413 (Largest even number strictly less than a square).
%K easy,sign
%O 1,2
%A Jerzy Kocik (jkocik(AT)siu.edu), Oct 03 2010
%E Edited by _Ray Chandler_, Dec 05 2011
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