Search: id:A003464
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%I A003464 M4425
%S A003464 1,7,43,259,1555,9331,55987,335923,2015539,12093235,72559411,435356467,
%T A003464 2612138803,15672832819,94036996915,564221981491,3385331888947,
%U A003464 20311991333683,121871948002099,731231688012595,4387390128075571
%N A003464 (6^n - 1)/5.
%C A003464 a(n) = A125118(n,5) for n>4. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 21 2006
%C A003464 a(n)=6*a(n-1)+1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Oct 29 2009]
%D A003464 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003464 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003464 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003464 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A003464 C. Banderier and D. Merlini, <a href="http://www.dsi.unifi.it/~merlini/
               poster.ps">Lattice paths with an infinite set of jumps</a>, FPSAC02, 
               Melbourne, 2002.
%H A003464 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=375">
               Encyclopedia of Combinatorial Structures 375</a>
%H A003464 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Repunit.html">Link to a section of The World of Mathematics.</a>
%F A003464 Binomial transform of A003948. If preceded by 0, then binomial transform 
               of powers of 5, A000351 (preceded by 0). - Paul Barry (pbarry(AT)wit.ie), 
               Mar 28 2003
%F A003464 a(n)=Sum{k=1..n, C(n, k)5^(k-1) }. E.g.f.: (exp(6x) - exp(x))/5 (offset 
               0). - Paul Barry (pbarry(AT)wit.ie), Mar 28 2003
%F A003464 G.f.: 1/((1-1x)(1-6x)) - Lambert Klasen (lambert.klasen(AT)gmx.net), 
               Feb 06 2005
%p A003464 a:=n->sum(6^(n-j),j=1..n): seq(a(n), n=1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 04 2007
%p A003464 A003464:=1/(6*z-1)/(z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
%p A003464 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=5*a[n-1]+6*a[n-2]+2 od: seq(a[n], 
               n=1..33);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 
               14 2008]
%t A003464 lst={};Do[p=(6^n-1)/5;AppendTo[lst, p], {n, 0, 5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Sep 29 2008]
%o A003464 (PARI) for(n=0,10,print1(polcoeff(1/((1-1*x)*(1-6*x)),n),",")) for(n=1,
               10,print1((6^n-1)/5,","))
%o A003464 (Other) sage: [lucas_number1(n,7,6) for n in xrange(1, 22)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
%o A003464 (Other) sage: [gaussian_binomial(n,1,6) for n in xrange(1,22)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
%Y A003464 Sequence in context: A043553 A049609 A161728 this_sequence A022036 A015451 
               A126502
%Y A003464 Adjacent sequences: A003461 A003462 A003463 this_sequence A003465 A003466 
               A003467
%K A003464 nonn,easy
%O A003464 1,2
%A A003464 N. J. A. Sloane (njas(AT)research.att.com).
%E A003464 More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Nov 21 2006

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