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 A096658 a(n) = (2^n)*a(n-1) + (2^(n-1))*a(n-2), a(0)=1, a(1)=2. 4
 1, 2, 10, 88, 1488, 49024, 3185152, 410836992, 105581969408, 54163142606848, 55517115997749248, 113754516621419872256, 466052199134899187220480, 3818365553813175477506932736, 62563919133290380117615296118784 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 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 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 *) CROSSREFS Cf. A000079, A096654, A096657, A233590. Sequence in context: A209884 A060350 A270923 * A186184 A326554 A055779 Adjacent sequences:  A096655 A096656 A096657 * A096659 A096660 A096661 KEYWORD nonn AUTHOR Clark Kimberling, Jul 01 2004 EXTENSIONS More terms from Benoit Cloitre, Jul 02 2004 STATUS approved

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Last modified October 21 03:07 EDT 2020. Contains 337910 sequences. (Running on oeis4.)