A096658 a(n) = (2^n)*a(n-1) + (2^(n-1))*a(n-2), a(0)=1, a(1)=2.

1, 2, 10, 88, 1488, 49024, 3185152, 410836992, 105581969408, 54163142606848, 55517115997749248, 113754516621419872256, 466052199134899187220480, 3818365553813175477506932736, 62563919133290380117615296118784

Offset: 0

Author

Clark Kimberling, Jul 01 2004

Keywords

• nonn

Comments

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.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..81

Crossrefs

Cf. A000079, A096654, A096657, A233590.

Programs

Mathematica

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 *)
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 *)

Formula

a(n) is asymptotic to c*2^(n(n+1)/2) where c=1.54241381761010214381886547... - Benoit Cloitre, Jul 01 2004

c = (1 + Sum_{k>=1} (Product_{j=1..k} 1/(2^(j-1)*(2^j-1)))) / A233590 = 1.5424138176101021438188654719396629292944606799275904286064... . - Vaclav Kotesovec, Nov 27 2015

Extensions

More terms from Benoit Cloitre, Jul 02 2004