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A028994 Even 10-gonal (or decagonal) numbers. 10
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, 24102, 25360, 26650, 27972 (list; graph; refs; listen; history; text; internal format)
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(m-1)[(m-1)(2n-1)+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)/(x-1)^3. - Colin Barker, Nov 18 2012

Sum_{n>=1} 1/a(n) = (8*log(2) - (sqrt(2)-1)*Pi - 2*sqrt(2)*log(1+sqrt(2)))/12. - Amiram Eldar, Feb 27 2022

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*n-3) \\ 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

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Last modified August 10 04:49 EDT 2022. Contains 356029 sequences. (Running on oeis4.)