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 A195041 Concentric heptagonal numbers. 8
 0, 1, 7, 15, 28, 43, 63, 85, 112, 141, 175, 211, 252, 295, 343, 393, 448, 505, 567, 631, 700, 771, 847, 925, 1008, 1093, 1183, 1275, 1372, 1471, 1575, 1681, 1792, 1905, 2023, 2143, 2268, 2395, 2527, 2661, 2800, 2941, 3087, 3235, 3388, 3543 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A033582 and A069127 interleaved. Partial sums of A047336. - 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) = 7*n^2/4 + 3*((-1)^n - 1)/8. From R. J. Mathar, Sep 28 2011: (Start) G.f.: -x*(1+5*x+x^2) / ( (1+x)*(x-1)^3 ). a(n) + a(n+1) = A069099(n+1). (End) a(n) = n^2 + floor(3*n^2/4). - Bruno Berselli, Aug 08 2013 Sum_{n>=1} 1/a(n) = Pi^2/42 + tan(sqrt(3/7)*Pi/2)*Pi/sqrt(21). - Amiram Eldar, Jan 16 2023 MATHEMATICA CoefficientList[Series[-((x (1+5 x+x^2))/((-1+x)^3 (1+x))), {x, 0, 80}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {0, 1, 7, 15}, 80] (* Harvey P. Dale, Jan 18 2021 *) PROG (Magma) [7*n^2/4+3*((-1)^n-1)/8: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011 (Haskell) a195041 n = a195041_list !! n a195041_list = scanl (+) 0 a047336_list -- Reinhard Zumkeller, Jan 07 2012 (PARI) a(n)=7*n^2\4 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Column 7 of A195040. Cf. A032527, A032528, A033582, A047336, A069099, A069127, A077221, A195042. Sequence in context: A239934 A193553 A274090 * A229462 A302125 A006188 Adjacent sequences: A195038 A195039 A195040 * A195042 A195043 A195044 KEYWORD nonn,easy AUTHOR Omar E. Pol, Sep 27 2011 STATUS approved

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Last modified February 5 18:47 EST 2023. Contains 360087 sequences. (Running on oeis4.)