This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A256944 #86 Jan 31 2024 07:50:31
%S A256944 0,1,4,9,16,36,49,64,100,144,196,256,289,324,400,484,576,676,784,900,
%T A256944 1024,1156,1296,1444,1600,1681,1764,1936,2116,2304,2500,2704,2916,
%U A256944 3136,3364,3600,3844,4096,4356,4624,4900,5184,5476,5776,6084,6400,6724,7056,7396,7744,8100,8464
%N A256944 Squares which are not the sums of two consecutive nonsquares.
%C A256944 The union of A008843, A055792, and A016742. [Corrected by _Charles R Greathouse IV_, May 07 2015]
%C A256944 Consists of the squares of all even numbers and odd numbers in A078057 = (1, 3, 7, 17, 41, 99, ...), see also A001333 = abs(A123335). See A257282 for the square roots and A257292 for their complement in the nonnegative integers A001477. - _M. F. Hasler_, May 08 2015
%H A256944 Charles R Greathouse IV, <a href="/A256944/b256944.txt">Table of n, a(n) for n = 1..10000</a>
%F A256944 a(n) ~ 4n^2. - _Charles R Greathouse IV_, May 07 2015
%F A256944 a(n) = A257282(n)^2. - _M. F. Hasler_, May 08 2015
%e A256944 0, 1, 4, 9, 16, 36, are in this sequence because first 14 sums of two consecutive nonsquares are 5, 8, 11, 13, 15, 18, 21, 23, 25, 27, 29, 32, 35, 37.
%t A256944 lim = 15000; s = Plus @@@ (Partition[#, 2, 1] & @ Complement[Range@ lim, Range[Floor@ Sqrt[lim]]^2]); Select[Range@ Floor[Sqrt[lim]]^2, !MemberQ[s, #] &] (* _Michael De Vlieger_, Apr 29 2015 *)
%t A256944 lst=Partition[Select[Range[0,10^6],!IntegerQ[Sqrt[#]]&],2,1]/.{a_,b_}-> a+b;a256944=Complement[Table[n^2,{n,0,Sqrt[Last[lst]]}],lst] (* timing improved by _Ivan N. Ianakiev_, Apr 30 2015 *)
%t A256944 Union[#, Range[0, Max@ #, 2]] &@ Numerator[Convergents[Sqrt@ 2, 6]]^2 (* _Michael De Vlieger_, Aug 06 2016, after _Harvey P. Dale_ at A001333 *)
%o A256944 (PARI) is(n)=issquare(n) && (n%2==0 || issquare(n\2) || issquare(n\2+1)) \\ _Charles R Greathouse IV_, May 07 2015
%Y A256944 Cf. A000037, A000290, A008843, A016742, A056792, A257282.
%K A256944 nonn,easy
%O A256944 1,3
%A A256944 _Juri-Stepan Gerasimov_, Apr 25 2015