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A247313 a(n) = 5*a(n-1) - 2^n for n>0, a(0)=1.

%I A247313 #26 Sep 08 2022 08:46:09
%S A247313 1,3,11,47,219,1063,5251,26127,130379,651383,3255891,16277407,
%T A247313 81382939,406906503,2034516131,10172547887,50862673899,254313238423,
%U A247313 1271565929971,6357829125567,31789144579259,158945720799143,794728599801411,3973642990618447
%N A247313 a(n) = 5*a(n-1) - 2^n for n>0, a(0)=1.
%D A247313 James Boswell Instituut, Sequences, 2006, p. 19 (recurrence 1.d).
%H A247313 Vincenzo Librandi, <a href="/A247313/b247313.txt">Table of n, a(n) for n = 0..1000</a>
%H A247313 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-10).
%F A247313 G.f.: (1-4*x)/((1-2*x)*(1-5*x)).
%F A247313 a(n) = ( 2^(n+1) + 5^n )/3.
%F A247313 a(n) = 7*a(n-1) - 10*a(n-2) for n>1.
%t A247313 RecurrenceTable[{a[0] == 1, a[n] == 5 a[n - 1] - 2^n}, a, {n, 0, 30}] (* or *) Table[(2^(n + 1) + 5^n)/3, {n, 0, 30}]
%o A247313 (Magma) [(2^(n+1)+5^n)/3: n in [0..30]];
%o A247313 (PARI) Vec((1-4*x)/((1-2*x)*(1-5*x)) + O(x^50)) \\ _Michel Marcus_, Sep 13 2014
%Y A247313 Cf. A000079, A000351, A074600, A085279.
%K A247313 nonn,easy
%O A247313 0,2
%A A247313 _Vincenzo Librandi_, Sep 12 2014