Search: id:A002452
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%I A002452 M4733 N2025
%S A002452 1,10,91,820,7381,66430,597871,5380840,48427561,435848050,3922632451,
%T A002452 35303692060,317733228541,2859599056870,25736391511831,231627523606480,
%U A002452 2084647712458321,18761829412124890,168856464709124011
%N A002452 (9^n - 1)/8.
%C A002452 Comment from David W. Wilson: Numbers triangular, differences square.
%C A002452 Partial sums of A001019. This is m-th triangular number, where m is partial 
               sums of A000244. a(n)=A000217(A003462(n)). - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               May 25 2004
%C A002452 With offset 0, binomial transform of A003951 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jul 22 2005
%C A002452 Numbers in base 9: 1, 11, 111, 1111, 11111, 111111,1111111, etc. [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
%D A002452 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002452 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002452 A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index 
               of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford 
               and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 112.
%D A002452 J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
%D A002452 T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 36.
%D A002452 M. Ward, Note on divisibility sequences, Bull. Amer. Math. Soc., 42 (1936), 
               843-845.
%H A002452 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 A002452 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 A002452 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Repunit.html">Link to a section of The World of Mathematics.</a>
%H A002452 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A002452 a(n) = 9*a(n-1) + 1; a(1) = 1 . G.f.: x / ((1-x)*(1-9*x)) . - DELEHAM 
               Philippe (kolotoko(AT)wanadoo.fr), Mar 13 2004
%p A002452 a:=n->sum(9^(n-j),j=1..n): seq(a(n), n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 04 2007
%p A002452 A002452:=1/(9*z-1)/(z-1); [S. Plouffe in his 1992 dissertation.]
%t A002452 lst={};Do[p=(9^n-1)/8;AppendTo[lst, p], {n, 0, 5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Sep 29 2008]
%o A002452 (Other) sage: [lucas_number1(n,10,9) for n in xrange(1, 20)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
%o A002452 (Other) sage: [gaussian_binomial(n,1,9) for n in xrange(1,20)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
%o A002452 (Other) sage: [gaussian_binomial(2*n,1,3)/4 for n in xrange(1,20)] # 
               [From Zerinvary Lajosz (zerinvarylajos(AT)yahoo.com), May 28 2009]
%Y A002452 Right-hand column 1 in triangle A008958.
%Y A002452 Sequence in context: A143572 A002739 A079928 this_sequence A096261 A015455 
               A110410
%Y A002452 Adjacent sequences: A002449 A002450 A002451 this_sequence A002453 A002454 
               A002455
%K A002452 nonn,easy
%O A002452 1,2
%A A002452 N. J. A. Sloane (njas(AT)research.att.com).
%E A002452 More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004

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