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 A195042 Concentric 9-gonal numbers. 9
 0, 1, 9, 19, 36, 55, 81, 109, 144, 181, 225, 271, 324, 379, 441, 505, 576, 649, 729, 811, 900, 991, 1089, 1189, 1296, 1405, 1521, 1639, 1764, 1891, 2025, 2161, 2304, 2449, 2601, 2755, 2916, 3079, 3249, 3421, 3600, 3781, 3969, 4159, 4356, 4555, 4761, 4969, 5184, 5401, 5625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also concentric enneagonal numbers or concentric nonagonal numbers. A016766 and A069131 interleaved. Partial sums of A056020. - Reinhard Zumkeller, Jan 07 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA a(n) = (9*n^2 + 5/2*((-1)^n - 1))/4. From R. J. Mathar, Sep 28 2011: (Start) G.f.: -x*(1+7*x+x^2) / ( (1+x)*(x-1)^3 ). a(n) + a(n+1) = A060544(n+1). (End) Sum_{n>=1} 1/a(n) = Pi^2/54 + tan(sqrt(5)*Pi/6)*Pi/(3*sqrt(5)). - Amiram Eldar, Jan 16 2023 MATHEMATICA LinearRecurrence[{2, 0, -2, 1}, {0, 1, 9, 19}, 60] (* Harvey P. Dale, Nov 24 2019 *) PROG (Magma) [(9*n^2+5/2*((-1)^n-1))/4: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011 (Haskell) a195042 n = a195042_list !! n a195042_list = scanl (+) 0 a056020_list -- Reinhard Zumkeller, Jan 07 2012 (PARI) a(n)=(9*n^2+5/2*((-1)^n-1))/4 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Column 9 of A195040. Cf. A016766, A069131, A077221, A195041, A195142, A195043. Sequence in context: A274590 A051811 A034056 * A157034 A198590 A297396 Adjacent sequences: A195039 A195040 A195041 * A195043 A195044 A195045 KEYWORD nonn,easy,changed AUTHOR Omar E. Pol, Sep 27 2011 STATUS approved

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Last modified January 26 17:44 EST 2023. Contains 359833 sequences. (Running on oeis4.)