cp's OEIS Frontend

A201630 a(n) = a(n-1) + 2*a(n-2) with n>1, a(0)=2, a(1)=7.

%I A201630 #44 Feb 07 2025 08:29:27
%S A201630 2,7,11,25,47,97,191,385,767,1537,3071,6145,12287,24577,49151,98305,
%T A201630 196607,393217,786431,1572865,3145727,6291457,12582911,25165825,
%U A201630 50331647,100663297,201326591,402653185,805306367,1610612737,3221225471,6442450945,12884901887
%N A201630 a(n) = a(n-1) + 2*a(n-2) with n>1, a(0)=2, a(1)=7.
%D A201630 B. Satyanarayana and K. S. Prasad, Discrete Mathematics and Graph Theory, PHI Learning Pvt. Ltd. (Eastern Economy Edition), 2009, p. 73 (problem 3.3).
%H A201630 Bruno Berselli, <a href="/A201630/b201630.txt">Table of n, a(n) for n = 0..1000</a>
%H A201630 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F A201630 G.f.: (2+5*x)/((1+x)*(1-2*x)).
%F A201630 a(n) = 3*2^n - (-1)^n.
%F A201630 a(n) = 7 + 2*Sum_{i=0..n-2} a(i), for n>0.
%F A201630 a(n) = A097581(A042948(n+1)).
%F A201630 a(n+2) - a(n) = a(n+1) + a(n) = A005010(n).
%F A201630 E.g.f.: 3*exp(2*x) - exp(-x). - _G. C. Greubel_, Feb 07 2025
%t A201630 LinearRecurrence[{1, 2}, {2,7}, 33]
%o A201630 (PARI) v=vector(33); v[1]=2; v[2]=7; for(i=3, #v, v[i]=v[i-1]+2*v[i-2]); v
%o A201630 (Magma) [n le 2 select 5*n-3 else Self(n-1)+2*Self(n-2): n in [1..33]];
%o A201630 (Maxima) a[0]:2$ a[1]:7$ a[n]:=a[n-1]+2*a[n-2]$ makelist(a[n], n, 0, 32);
%o A201630 (SageMath)
%o A201630 def A201630(n): return 3*2**n - (-1)**n
%o A201630 print([A201630(n) for n in range(31)]) # _G. C. Greubel_, Feb 07 2025
%Y A201630 Cf. A001045, A005010, A042948, A097581.
%K A201630 nonn,easy
%O A201630 0,1
%A A201630 _Bruno Berselli_, Dec 03 2011