|
%I #17 Feb 16 2020 12:51:56
%S 1,2,10,88,1488,49024,3185152,410836992,105581969408,54163142606848,
%T 55517115997749248,113754516621419872256,466052199134899187220480,
%U 3818365553813175477506932736,62563919133290380117615296118784
%N a(n) = (2^n)*a(n-1) + (2^(n-1))*a(n-2), a(0)=1, a(1)=2.
%C This is the sequence of denominators of self-convergents to the number 1.40861... (see A233590) whose self-continued fraction is (1,2,4,8,16,...). See A096657 for numerators and A096654 for definitions.
%H Harvey P. Dale, <a href="/A096658/b096658.txt">Table of n, a(n) for n = 0..81</a>
%F a(n) is asymptotic to c*2^(n(n+1)/2) where c=1.54241381761010214381886547... - _Benoit Cloitre_, Jul 01 2004
%F c = (1 + Sum_{k>=1} (Product_{j=1..k} 1/(2^(j-1)*(2^j-1)))) / A233590 = 1.5424138176101021438188654719396629292944606799275904286064... . - _Vaclav Kotesovec_, Nov 27 2015
%t a[0]=1; a[1]=2; a[n_] := (2^n)*a[n-1] + (2^(n-1))*a[n-2]; Table[ a[n], {n, 0, 14}] (* _Robert G. Wilson v_, Jul 03 2004 *)
%t RecurrenceTable[{a[0]==1,a[1]==2,a[n]==2^n a[n-1]+2^(n-1) a[n-2]},a,{n,20}] (* _Harvey P. Dale_, Feb 16 2020 *)
%Y Cf. A000079, A096654, A096657, A233590.
%K nonn
%O 0,2
%A _Clark Kimberling_, Jul 01 2004
%E More terms from _Benoit Cloitre_, Jul 02 2004
|
