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Search: id:A001106
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| A001106 |
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9-gonal (or enneagonal or nonagonal) numbers: n(7n-5)/2.
(Formerly M4604)
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+0
42
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| 0, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 396, 474, 559, 651, 750, 856, 969, 1089, 1216, 1350, 1491, 1639, 1794, 1956, 2125, 2301, 2484, 2674, 2871, 3075, 3286, 3504, 3729, 3961, 4200, 4446, 4699, 4959, 5226, 5500, 5781, 6069, 6364
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for sequences related to linear recurrences with constant coefficients
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.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 343
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=(7*n-5)*n/2. G.f.: x*(1+6*x)/(1-x)^3.
a(n)=n+7*A000217(n-1) - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 14 2005
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
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
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]
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]
a(n)=7*n+a(n-1)-13 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]
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EXAMPLE
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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]
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MAPLE
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A001106:=-(1+6*z)/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
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
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A093564 ((7, 1) Pascal, column m=2). Partial sums of A016993.
Cf. A131875.
Cf. A000217, A000567, A001107.
Sequence in context: A063066 A097658 A067725 this_sequence A023551 A022787 A079770
Adjacent sequences: A001103 A001104 A001105 this_sequence A001107 A001108 A001109
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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