cp's OEIS Frontend

A084330 a(0)=0, a(1)=1, a(n) = 31*a(n-1) - 29*a(n-2).

%I A084330 #32 Dec 16 2023 17:45:23
%S A084330 0,1,31,932,27993,840755,25251608,758417953,22778659911,684144336604,
%T A084330 20547893297305,617144506454939,18535590794481264,556706123941725953,
%U A084330 16720357709153547887,502186611389449931860,15082894579507494998937,453006320234438296943107
%N A084330 a(0)=0, a(1)=1, a(n) = 31*a(n-1) - 29*a(n-2).
%H A084330 Karl V. Keller, Jr., <a href="/A084330/b084330.txt">Table of n, a(n) for n = 0..1000</a>
%H A084330 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (31,-29).
%F A084330 a(n) = (1/13)*sum(k=0, n, binomial(n, k)*F(7*k)) where F(k) denotes the k-th Fibonacci number.
%F A084330 G.f.: x / (29*x^2-31*x+1). - _Colin Barker_, Jun 26 2013
%p A084330 f:=proc(n) option remember; if n <=1 then n else 31*f(n-1)-29*f(n-2); fi; end;
%t A084330 LinearRecurrence[{31,-29},{0,1},30] (* _Harvey P. Dale_, Jul 11 2014 *)
%o A084330 (PARI) a(n)=(1/13)*sum(k=0,n,binomial(n,k)*fibonacci(7*k))
%o A084330 (Magma) I:=[0,1]; [n le 2 select I[n] else 31*Self(n-1)-29*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jun 02 2015
%Y A084330 Cf. A030191.
%K A084330 nonn,easy
%O A084330 0,3
%A A084330 _Benoit Cloitre_, Jun 21 2003
%E A084330 Corrected by _N. J. A. Sloane_, Sep 16 2005