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 A195158 Concentric 24-gonal numbers. 6
 0, 1, 24, 49, 96, 145, 216, 289, 384, 481, 600, 721, 864, 1009, 1176, 1345, 1536, 1729, 1944, 2161, 2400, 2641, 2904, 3169, 3456, 3745, 4056, 4369, 4704, 5041, 5400, 5761, 6144, 6529, 6936, 7345, 7776, 8209, 8664, 9121, 9600, 10081, 10584, 11089 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence found by reading the line from 0, in the direction 0, 24, ..., and the same line from 1, in the direction 1, 49, ..., in the square spiral whose vertices are the generalized tetradecagonal numbers A195818. Main axis, perpendicular to A049598 in the same spiral. 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) = 6*n^2 + 5*((-1)^n-1)/2. a(n) = -a(n-1) + A069190(n). - Vincenzo Librandi, Sep 30 2011 From Colin Barker, Sep 16 2012: (Start) a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). G.f.: x*(1+22*x+x^2)/((1-x)^3*(1+x)). (End) Sum_{n>=1} 1/a(n) = Pi^2/144 + tan(sqrt(5/6)*Pi/2)*Pi/(4*sqrt(30)). - Amiram Eldar, Jan 17 2023 MATHEMATICA LinearRecurrence[{2, 0, -2, 1}, {0, 1, 24, 49}, 50] (* Harvey P. Dale, Jan 28 2021 *) PROG (Magma) [(12*n^2+5*(-1)^n-5)/2: n in [0..50]]; // Vincenzo Librandi, Sep 30 2011 (PARI) a(n)=6*n^2+5*((-1)^n-1)/2 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Column 24 of A195040. Cf. A032527, A032528, A195143, A195149, A195058. Sequence in context: A044482 A045294 A258366 * A045279 A042142 A042144 Adjacent sequences: A195155 A195156 A195157 * A195159 A195160 A195161 KEYWORD nonn,easy AUTHOR Omar E. Pol, Sep 28 2011 STATUS approved

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Last modified August 6 18:55 EDT 2024. Contains 374981 sequences. (Running on oeis4.)