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A200859 a(n) = 2*a(n-1)+3*a(n-2)+5^n for n>1, a(0)=-2, a(1)=1.

%I A200859 #37 Mar 29 2024 05:43:49
%S A200859 -2,1,21,170,1028,5691,30091,155380,791658,4002581,20145761,101127390,
%T A200859 506832688,2537750671,12699515031,63529860200,317746156118,
%U A200859 1589021345961,7945978425901,39732507217810,198670381353948,993375442564451,4966947820206371,24834950923184220
%N A200859 a(n) = 2*a(n-1)+3*a(n-2)+5^n for n>1, a(0)=-2, a(1)=1.
%D A200859 B. Satyanarayana and K. S. Prasad, Discrete Mathematics and Graph Theory, PHI Learning Pvt. Ltd. (Eastern Economy Edition), 2009, p. 81 (3.1;4)
%H A200859 Bruno Berselli, <a href="/A200859/b200859.txt">Table of n, a(n) for n = 0..1000</a>.
%H A200859 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,-15).
%F A200859 G.f.: -(2-15*x)/((1+x)*(1-3*x)*(1-5*x)).
%F A200859 a(n) = 7*a(n-1)-7*a(n-1)-15*a(n-3) for n>2, a(0)=-2, a(1)=1, a(2)=21.
%F A200859 a(n) = (50*5^n-81*3^n-17*(-1)^n)/24.
%p A200859 A200859:=n->(50*5^n-81*3^n-17*(-1)^n)/24; seq(A200859(n), n=0..30); # _Wesley Ivan Hurt_, Dec 26 2013
%t A200859 LinearRecurrence[{7,-7,-15}, {-2,1,21}, 24]
%t A200859 nxt[{n_,a_,b_}]:={n+1,b,2b+3a+5^(n+1)}; NestList[nxt,{1,-2,1},30][[All,2]] (* _Harvey P. Dale_, Dec 28 2021 *)
%o A200859 (Magma) [n le 2 select 3*n-5 else 2*Self(n-1)+3*Self(n-2)+5^(n-1): n in [1..24]];
%o A200859 (PARI) for(n=0, 23, print1((50*5^n-81*3^n-17*(-1)^n)/24", "));
%o A200859 (Maxima) makelist(coeff(taylor(-(2-15*x)/((1+x)*(1-3*x)*(1-5*x)), x, 0, n), x, n), n, 0, 23);
%o A200859 (Sage)
%o A200859 def lr(a0, a1, a2, a3, a4, a5):
%o A200859     x, y, z = a0, a1, a2
%o A200859     while True:
%o A200859        yield x
%o A200859        x, y, z = y, z, a5*x+a4*y+a3*z
%o A200859 A200859 = lr(-2, 1, 21, 7, -7, -15)
%o A200859 print([next(A200859) for n in range(24)]) # _Bruno Berselli_, May 09 2014
%Y A200859 Cf. A016209, A200864.
%K A200859 sign,easy
%O A200859 0,1
%A A200859 _Bruno Berselli_, Nov 23 2011