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A305559 [0, -1, -1] together with A000290.

%I A305559 #37 May 28 2025 10:51:19
%S A305559 0,-1,-1,0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,
%T A305559 324,361,400,441,484,529,576,625,676,729,784,841,900,961,1024,1089,
%U A305559 1156,1225,1296,1369,1444,1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,2401,2500
%N A305559 [0, -1, -1] together with A000290.
%C A305559 Squares leading to an autosequence of the first kind.
%C A305559 The third sequence of the array
%C A305559 A060576(n+1)=         0,  1, 1,  1,  1,   1,   1,   1,   1,  1, ...
%C A305559 A289207(n)=      0,   0,  0, 1,  2,  3,   4,   5,   6,   7, ...
%C A305559 a(n)=       0,  -1,  -1,  0, 1,  4,  9,  16,  25,  36, ...
%C A305559       0,   10,  10,   5,  0, 1,  8, 27,  64, 125, ...
%C A305559 0, -113, -113, -68, -23,  0, 1, 16, 81, 256, ... .
%C A305559 The first full vertical is (-1)^n*A033312(n).
%C A305559 From 0, the first two nonzero antidiagonals are 0, -1, 10, -113, 1526, ... = (-1)^n* A176824(n+1).
%C A305559 See OEIS Wiki, Autosequence.
%C A305559 a(n) difference table:
%C A305559 0, -1, -1, 0, 1, 4, 9, 16, 25, ...
%C A305559 -1, 0,  1, 1, 3, 5, 7,  9, 11, ...
%C A305559 1,  1,  0, 2, 2, 2, 2,  2,  2, ...
%C A305559 0, -1,  2, 0, 0, 0, 0,  0,  0, ...
%H A305559 Paolo Xausa, <a href="/A305559/b305559.txt">Table of n, a(n) for n = 0..1000</a>
%H A305559 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A305559 From _Stefano Spezia_, May 28 2025: (Start)
%F A305559 G.f.: x*(1 - 2*x + x^3 - 2*x^4)/(1 - x)^3.
%F A305559 E.g.f.: 9 + 5*x + x^2 - exp(x)*(9 - 5*x + x^2). (End)
%t A305559 Join[{0,-1,-1},Range[0,100]^2] (* _Paolo Xausa_, Nov 13 2023 *)
%Y A305559 Cf. A003992, A033312, A060576, A176824, A289207, A000290, A113679.
%K A305559 sign,easy,less
%O A305559 0,6
%A A305559 _Paul Curtz_, Jun 21 2018