

A028994


Even 10gonal (or decagonal) numbers.


9



0, 10, 52, 126, 232, 370, 540, 742, 976, 1242, 1540, 1870, 2232, 2626, 3052, 3510, 4000, 4522, 5076, 5662, 6280, 6930, 7612, 8326, 9072, 9850, 10660, 11502, 12376, 13282, 14220, 15190, 16192, 17226, 18292, 19390, 20520, 21682, 22876
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OFFSET

0,2


COMMENTS

a(n) (for n >= 1) is also the Wiener index of the windmill graph D(5, n). The windmill graph D(m, n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e. a bouquet of n pieces of K_m graphs). The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph. The Wiener index of D(m, n) is (1/2)n(m1)[(m1)(2n1)+1]. For the Wiener indices of D(3, n), D(4, n), and D(6, n) see A033991, A152743, and A180577, respectively.  Emeric Deutsch, Sep 21 2010


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Decagonal Number
Eric Weisstein's World of Mathematics, Windmill Graph  Emeric Deutsch, Sep 21 2010
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 2*n*(8*n  3).  Omar E. Pol, Aug 19 2011
G.f.: 2*x*(11*x+5)/(x1)^3.  Colin Barker, Nov 18 2012


MATHEMATICA

CoefficientList[Series[2 x (11 x + 5)/(x  1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 18 2013 *)
LinearRecurrence[{3, 3, 1}, {0, 10, 52}, 40] (* Harvey P. Dale, Dec 10 2014 *)
Table[16n^2  6n, {n, 0, 49}] (* Alonso del Arte, Jan 24 2017 *)


PROG

(MAGMA) [2*n*(8*n  3): n in [0..60]]; // Vincenzo Librandi, Oct 18 2013
(PARI) a(n)=2*n*(8*n3) \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Cf. A033991, A152743, A180577, A001107, A028993, A139273.
Sequence in context: A041186 A058827 A232909 * A257042 A092966 A281401
Adjacent sequences: A028991 A028992 A028993 * A028995 A028996 A028997


KEYWORD

nonn,easy


AUTHOR

Patrick De Geest


STATUS

approved



