Search: id:A015565
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%I A015565
%S A015565 0,1,7,57,455,3641,29127,233017,1864135,14913081,119304647,954437177,
%T A015565 7635497415,61083979321,488671834567,3909374676537,31274997412295,
%U A015565 250199979298361,2001599834386887,16012798675095097,128102389400760775
%N A015565 a(n) = 7 a(n-1) + 8 a(n-2).
%C A015565 A linear 2nd order recurrence. A Jacobsthal number sequence.
%C A015565 Second binomial transform of A080424. Binomial transform of A053573, 
               with leading zero. Binomial transform is 0,1,9,81,729,....(9^n/9-0^n/
               9). Second binomial transform is 0,1,11,111,1111,... (A002275: repunits). 
               - Paul Barry (pbarry(AT)wit.ie), Mar 14 2004
%C A015565 Number of walks of length n between any two distinct nodes of the complete 
               graph K_9. Example: a(2)=7 because the walks of length 2 between 
               the nodes A and B of the complete graph ABCDEFGHI are: ACB, ADB, 
               AEB, AFB, AGB, AHB and AIB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 01 2004
%C A015565 Unsigned version of A014990 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Feb 13 2007
%C A015565 General form: k=8^n-k. Also: A001045, A078008, A097073, A115341, A015518, 
               A054878, A015521, A109499, A015531, A109500, A109501, A015552 [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
%F A015565 a(n)=8^n/9-(-1)^n/9. a(n)=J(3n)/3=A001045(3n)/3. Binomial transform of 
               A053573 (preceded by zero). - Paul Barry (pbarry(AT)wit.ie), Apr 
               09 2003
%F A015565 a(n)=8^(n-1)-a(n-1). G.f.=x/(1-7x-8x^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Apr 01 2004
%F A015565 a(n)=Sum_{k, 0<=k<=n} A106566(n,k)*A099322(k). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 30 2008]
%t A015565 k=0;lst={k};Do[k=8^n-k;AppendTo[lst, k], {n, 0, 5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
%o A015565 (Other) sage: [lucas_number1(n,7,-8) for n in xrange(0, 21)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
%Y A015565 Cf. A082311, A082365.
%Y A015565 Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, 
               A015531, A109500, A109501, A015552 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Dec 11 2008]
%Y A015565 Sequence in context: A042187 A082310 A014990 this_sequence A082413 A142990 
               A147689
%Y A015565 Adjacent sequences: A015562 A015563 A015564 this_sequence A015566 A015567 
               A015568
%K A015565 nonn,easy
%O A015565 0,3
%A A015565 Olivier Gerard (olivier.gerard(AT)gmail.com)

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