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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
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
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
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