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 A167149 10000-gonal numbers: a(n) = n + 4999 * n * (n-1). 2
 0, 1, 10000, 29997, 59992, 99985, 149976, 209965, 279952, 359937, 449920, 549901, 659880, 779857, 909832, 1049805, 1199776, 1359745, 1529712, 1709677, 1899640, 2099601, 2309560, 2529517, 2759472, 2999425, 3249376, 3509325, 3779272, 4059217, 4349160, 4649101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS There are infinitely many 10000-gonal numbers that are also squares. The first seven are at n = 0, 1, 2, 21, 9800, 173774514938177, 1042188013912456. - Muniru A Asiru, Apr 10 2016 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA From R. J. Mathar, Nov 02 2009: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). G.f.: x*(1 + 9997*x)/(1-x)^3. (End) E.g.f.: exp(x)*x*(1 + 4999*x). - Ilya Gutkovskiy, Apr 10 2016 MAPLE P := proc(n, k) n*((k-2)*n-k+4)/2 ; end: A167149 := proc(n) P(n, 10000) ; end: seq(A167149(n), n=0..50) ; # R. J. Mathar, Nov 02 2009 MATHEMATICA Table[n + 4999 n (n - 1), {n, 0, 31}] (* or *) CoefficientList[Series[x (1 + 9997 x)/(1 - x)^3, {x, 0, 31}], x] (* Michael De Vlieger, Apr 10 2016 *) LinearRecurrence[{3, -3, 1}, {0, 1, 10000}, 10] (* G. C. Greubel, Jun 04 2016 *) PROG (PARI) x='x+O('x^99); concat(0, Vec(x*(1+9997*x)/(1-x)^3)) \\ Altug Alkan, Apr 10 2016 (GAP) A167149:=List([1..10^2], n->n+499*n*(n-1)); # Muniru A Asiru, Sep 27 2017 CROSSREFS Cf. A057145. - R. J. Mathar, Nov 02 2009 Sequence in context: A004270 A168651 A043492 * A277398 A326640 A017176 Adjacent sequences:  A167146 A167147 A167148 * A167150 A167151 A167152 KEYWORD nonn,easy AUTHOR Michael G. Fenner (sidk.20c(AT)gmail.com), Oct 28 2009 EXTENSIONS Edited (but not checked) by N. J. A. Sloane, Nov 01 2009 Sequence extended by R. J. Mathar, Nov 02 2009 STATUS approved

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Last modified October 15 13:06 EDT 2019. Contains 328030 sequences. (Running on oeis4.)