Search: id:A001106
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%I A001106 M4604
%S A001106 0,1,9,24,46,75,111,154,204,261,325,396,474,559,651,750,856,969,
%T A001106 1089,1216,1350,1491,1639,1794,1956,2125,2301,2484,2674,2871,3075,
%U A001106 3286,3504,3729,3961,4200,4446,4699,4959,5226,5500,5781,6069,6364
%N A001106 9-gonal (or enneagonal or nonagonal) numbers: n(7n-5)/2.
%D A001106 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001106 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.
%D A001106 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 189.
%H A001106 T. D. Noe, <a href="b001106.txt">Table of n, a(n) for n=0..1000</a>
%H A001106 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A001106 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 A001106 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 A001106 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=343">
               Encyclopedia of Combinatorial Structures 343</a>
%H A001106 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NonagonalNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A001106 a(n)=(7*n-5)*n/2. G.f.: x*(1+6*x)/(1-x)^3.
%F A001106 a(n)=n+7*A000217(n-1) - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 
               14 2005
%F A001106 Starting (1, 9, 24, 46, 75,...) gives the binomial transform of (1, 8, 
               7, 0, 0, 0,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 22 
               2007
%F A001106 Row sums of triangle A131875 starting (1, 9, 24, 46, 75, 111,...). A001106 
               = binomial transform of (1, 8, 7, 0, 0, 0,...). - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Jul 22 2007
%F A001106 a(n)=3a(n-1)-3a(n-2)+a(n-3), a(0)=0, a(1)=1, a(2)=9 [From Jaume Oliver 
               Lafont (joliverlafont(AT)gmail.com), Dec 02 2008]
%F A001106 Also, let Nn(n) = 9-gonal numbers, T(n)=triangular numbers, then Nn(n) 
               = T(n)+6*T(n-1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Jan 28 2009]
%F A001106 a(n)=7*n+a(n-1)-13 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 12 2009]
%e A001106 For n=2, a(2)=7*2+0-13=1; n=3, a(3)=7*3+1-13=9; n=4, a(4)=7*4+9-13=24 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
%p A001106 A001106:=-(1+6*z)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
%p A001106 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+7 od: seq(a[n], 
               n=0..43); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 
               2008
%t A001106 s=0;lst={s};Do[s+=n++ +1;AppendTo[lst, s], {n, 0, 6!, 7}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]
%Y A001106 Cf. A093564 ((7, 1) Pascal, column m=2). Partial sums of A016993.
%Y A001106 Cf. A131875.
%Y A001106 Cf. A000217, A000567, A001107.
%Y A001106 Sequence in context: A063066 A097658 A067725 this_sequence A023551 A022787 
               A079770
%Y A001106 Adjacent sequences: A001103 A001104 A001105 this_sequence A001107 A001108 
               A001109
%K A001106 nonn,easy,nice
%O A001106 0,3
%A A001106 N. J. A. Sloane (njas(AT)research.att.com).

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