Search: id:A015519
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%I A015519
%S A015519 0,1,2,11,36,149,550,2143,8136,31273,119498,457907,1752300,6709949,
%T A015519 25685998,98341639,376485264,1441362001,5518120850,21125775707,
%U A015519 80878397364,309637224677,1185423230902,4538307034543,17374576685400
%N A015519 a(n) = 2 a(n-1) + 7 a(n-2).
%C A015519 a(n)=a(n-1)+A083100(n-2), n>1. A083100(n)/a(n+1) converges to sqrt(8). 
               - Mario Catalani (mario.catalani(AT)unito.it), Apr 23 2003
%C A015519 The same sequence may be obtained by the following process. Starting 
               a priori with the fraction 1/1, the denominators of fractions built 
               according to the rule: add top and bottom to get the new bottom, 
               add top and 8 times the bottom to get the new top. The limit of the 
               sequence of fractions is sqrt(8). - Cino Hilliard (hillcino368(AT)gmail.com), 
               Sep 25 2005
%D A015519 John Derbyshire, Prime Obsession, Joseph Henry Press, April 2004, see 
               p. 16.
%F A015519 G.f.: x/((1-(1+sqrt(8))x)(1-(1-sqrt(8))x)); a(n) := ((1+2sqrt(2))^n-(1-2sqrt(2))^n)sqrt(2)/
               8. - Paul Barry (pbarry(AT)wit.ie), Jul 17 2003
%F A015519 E.g.f. : exp(x)sinh(2sqrt(2)x)/(2sqrt(2)). - Paul Barry (pbarry(AT)wit.ie), 
               Nov 20 2003
%F A015519 Second binomial transform is A000129(2n)/2 (A001109). - Paul Barry (pbarry(AT)wit.ie), 
               Apr 21 2004
%F A015519 a(n)=sum(comb(n-k-1, k)(7/2)^k2^(n-k-1), k, 0, floor((n-1)/2)). - Paul 
               Barry (pbarry(AT)wit.ie), Jul 17 2004
%F A015519 a(n)=sum{k=0..n, binomial(n, 2k+1)8^k} - Paul Barry (pbarry(AT)wit.ie), 
               Sep 29 2004
%o A015519 (Other) sage: [lucas_number1(n,2,-7) for n in xrange(0, 25)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
%Y A015519 The following sequences (and others) belong to the same family: A001333, 
               A000129, A026150, A002605, A046717, A015518, A084057, A063727, A002533, 
               A002532, A083098, A083099, A083100, A015519.
%Y A015519 Sequence in context: A154416 A071244 A005583 this_sequence A096977 A084098 
               A152819
%Y A015519 Adjacent sequences: A015516 A015517 A015518 this_sequence A015520 A015521 
               A015522
%K A015519 nonn,easy
%O A015519 0,3
%A A015519 Olivier Gerard (olivier.gerard(AT)gmail.com)

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