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A028994
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Even 10-gonal (or decagonal) numbers.
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10
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A033991, A152743, A180577, A001107, A028993, A139273.
Sequence in context: A041186 A058827 A232909 * A257042 A092966 A281401
Adjacent sequences: A028991 A028992 A028993 * A028995 A028996 A028997
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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