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A195163
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1000-gonal numbers: a(n) = n*(499*n - 498).
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4
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0, 1, 1000, 2997, 5992, 9985, 14976, 20965, 27952, 35937, 44920, 54901, 65880, 77857, 90832, 104805, 119776, 135745, 152712, 170677, 189640, 209601, 230560, 252517, 275472, 299425, 324376, 350325, 377272, 405217, 434160, 464101, 495040, 526977, 559912, 593845, 628776
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = 998*n*(n-1)/2 + n, according to the common formula for s-gonal numbers, a(n) = (s-2)*n*(n-1)/2 + n. - Sergey Pavlov, Aug 14 2015
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. - Muniru A Asiru, Sep 12 2017
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MAPLE
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MATHEMATICA
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PROG
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(PARI) x='x+O('x^99); concat(0, Vec(x*(1+997*x)/(1-x)^3)) \\ Altug Alkan, Apr 10 2016
(JavaScript) function a(n){return 998*n*(n-1)/2+n} // Sergey Pavlov, Aug 14 2015
(GAP)
a:=[0, 1, 1000];; for n in [4..10^2] do a[n]:=3*a[n-1]-3*a[n-2]+*a[n-3]; od; a; # Muniru A Asiru, Sep 12 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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