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%I #22 Sep 08 2022 08:45:09
%S 1,7,41,223,1169,6007,30521,154063,774689,3886567,19472201,97479103,
%T 487749809,2439811927,12202248281,61020807343,305132734529,
%U 1525749766087,7629007110761,38145810394783,190731376496849
%N a(n) = 2*5^n - 3^n.
%C Binomial transform of A016516. Inverse binomial transform of A081626.
%C Row sums of the triangle of 2^n terms shown in A178590 appears to = A081625. - _Gary W. Adamson_, May 29 2010
%C Binomial transform of A006516: (1, 6, 28, 120, 496, ...). - _Gary W. Adamson_, May 31 2010
%H Vincenzo Librandi, <a href="/A081625/b081625.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-15).
%F a(n) = 8*a(n-1) - 15*a(n-2), a(0)=1, a(1)=7.
%F G.f.: (1-x)/((1-3*x)(1-5*x)).
%F E.g.f. 2*exp(5*x) - exp(3*x).
%F a(n) = Sum_{k=0..n} A125185(n,k)*3^k. - _Philippe Deléham_, Feb 26 2012
%t CoefficientList[Series[(1 - x) / ((1 - 3 x) (1 - 5 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 09 2013 *)
%t LinearRecurrence[{8,-15},{1,7},30] (* _Harvey P. Dale_, Oct 14 2013 *)
%o (Magma) [2*5^n-3^n: n in [0..25]]; // _Vincenzo Librandi_, Aug 09 2013
%Y Cf. A178590, A006516.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 25 2003
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