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%I #43 Jun 22 2023 15:01:52
%S 1,0,-3,-8,-15,-24,-35,-48,-63,-80,-99,-120,-143,-168,-195,-224,-255,
%T -288,-323,-360,-399,-440,-483,-528,-575,-624,-675,-728,-783,-840,
%U -899,-960,-1023,-1088,-1155,-1224,-1295,-1368,-1443,-1520,-1599,-1680,-1763,-1848
%N a(n) = 1 - n^2.
%H G. C. Greubel, <a href="/A258837/b258837.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (1-3*x)/(1-x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F a(n) = -A067998(n+1). - _Joerg Arndt_, Jun 13 2015
%F a(n) = (-1)^n*A131386(n+1). - _Bruno Berselli_, Jun 15 2015
%F E.g.f.: (1 - x - x^2)*exp(x). - _G. C. Greubel_, May 11 2017
%F Sum_{n>=2} 1/a(n) = -3/4. - _Amiram Eldar_, Feb 17 2023
%t Table[1 - n^2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 0, -3}, 50]
%o (Magma) [1-n^2: n in [0..50]] /* or */ I:=[1,0,-3]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]];
%o (PARI) my(x='x+O('x^50)); Vec((1-3*x)/(1-x)^3) \\ _G. C. Greubel_, May 11 2017
%Y Cf. A067998, A131386, A007531.
%Y Sequences of the type 1-n^k: A024000 (k=1), this sequence (k=2), A024001 (k=3), A024002 (k=4), A024003 (k=5), A024004 (k=6), A024005 (k=7), A024006 (k=8), A024007 (k=9), A024008 (k=10), A024009 (k=11), A024010 (k=12).
%K sign,easy
%O 0,3
%A _Vincenzo Librandi_, Jun 12 2015
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