%I #31 Sep 08 2022 08:46:18
%S 0,1,-3,-26,699,56593,-13751400,-10024714007,21924035781909,
%T 143843588740390942,-2831273335253079129477,
%U -167183859029515480776096431,29616119072670305537790075332880,15739219935931795986279179944204983649,-25093400345884972653159910700646932070891747
%N a(n) = (-3)^(n-1)*a(n-1) + a(n-2).
%H Seiichi Manyama, <a href="/A280222/b280222.txt">Table of n, a(n) for n = 0..65</a>
%e G.f. = x - 3*x^2 - 26*x^3 + 699*x^4 + 56593*x^5 - 13751400*x^6 + ...
%t a[n_] := (-3)^(n -1) a[n -1] + a[n -2]; a[0] = 0; a[1] = 1; Array[a, 15, 0] (* _Robert G. Wilson v_, Dec 29 2016 *)
%t nxt[{n_,a_,b_}]:={n+1,b,b*(-3)^n+a}; NestList[nxt,{1,0,1},20][[All,2]] (* _Harvey P. Dale_, Jul 09 2018 *)
%o (Ruby)
%o def A(m, n)
%o i, a, b = 0, 0, 1
%o ary = [0]
%o while i < n
%o i += 1
%o a, b = b, b * m ** i + a
%o ary << a
%o end
%o ary
%o end
%o def A280222(n)
%o A(-3, n)
%o end
%o (PARI) m=20; v=concat([1, -3], vector(m-2)); for(n=3, m, v[n] = (-3)^(n-1)*v[n-1] + v[n-2]); concat([0],v) \\ _G. C. Greubel_, Oct 13 2018
%o (Magma) I:=[1,-3]; [0] cat [n le 2 select I[n] else (-3)^(n-1)*Self(n-1) +Self(n-2): n in [1..20]]; // _G. C. Greubel_, Oct 13 2018
%o (GAP) a:=[1,-3];; for n in [3..15] do a[n]:=(-3)^(n-1)*a[n-1]+a[n-2]; od; Concatenation([0],a); # _Muniru A Asiru_, Oct 19 2018
%Y Cf. similar sequences with the recurrence q^(n-1)*a(n-1) + a(n-2) for n>1, a(0)=0 and a(1)=1: this sequence (q=-3), A280221 (q=-2), A280261 (q=-1), A000045 (q=1), A015473 (q=2), A015474 (q=3), A015475 (q=4), A015476 (q=5), A015477 (q=6), A015479 (q=7), A015480 (q=8), A015481 (q=9), A015482 (q=10), A015484 (q=11).
%K sign
%O 0,3
%A _Seiichi Manyama_, Dec 29 2016
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