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A069130
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Centered 17-gonal numbers.
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5
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1, 18, 52, 103, 171, 256, 358, 477, 613, 766, 936, 1123, 1327, 1548, 1786, 2041, 2313, 2602, 2908, 3231, 3571, 3928, 4302, 4693, 5101, 5526, 5968, 6427, 6903, 7396, 7906, 8433, 8977, 9538, 10116, 10711, 11323, 11952, 12598, 13261, 13941, 14638, 15352
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OFFSET
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1,2
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COMMENTS
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Equals binomial transform of [1, 17, 17, 0, 0, 0,...] [From Gary W. Adamson, Mar 26 2010]
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LINKS
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Table of n, a(n) for n=1..43.
E. Weisstein, Centered Polygonal Numbers
Index entries for sequences related to centered polygonal numbers
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1)
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FORMULA
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a(n) = (17*n^2 - 17*n + 2)/2.
a(n) = 17*n+a(n-1)-17 (with a(1)=1) [From Vincenzo Librandi, Aug 08 2010]
G.f.: x*(1+15*x+x^2) / (1-x)^3 . - R. J. Mathar, Feb 04 2011
a(0)=1, a(1)=18, a(2)=52, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, June 05 2011]
Narayana transform (A001263) of [1, 17, 0, 0, 0,...]. - Gary W. Adamson, Jul 28, 2011
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EXAMPLE
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a(5) = 171 because (17*5^2 - 17*5 + 2)/2 = (425 - 85 + 2)/2 = 342/2 = 171.
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MATHEMATICA
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FoldList[#1 + #2 &, 1, 17 Range@ 45] (*Robert G. Wilson v, Feb 02 2011 *)
Table[(17n^2-17n+2)/2, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 18, 52}, 50] (* From Harvey P. Dale, June 05 2011 *)
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PROG
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(PARI) a(n)=17*binomial(n, 2)+1 \\ Charles R Greathouse IV, Jun 05 2011
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CROSSREFS
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Cf. A005448, A001844, A005891, A003215, A069099.
Sequence in context: A093520 A051870 A175815 * A124711 A126372 A133356
Adjacent sequences: A069127 A069128 A069129 * A069131 A069132 A069133
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KEYWORD
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easy,nice,nonn,changed
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AUTHOR
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Terrel Trotter, Jr., Apr 07 2002
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EXTENSIONS
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Typo in formula fixed by Omar E. Pol, Dec 22 2008
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STATUS
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approved
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