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 A051876 24-gonal numbers: a(n) = n*(11*n-10). 11
 0, 1, 24, 69, 136, 225, 336, 469, 624, 801, 1000, 1221, 1464, 1729, 2016, 2325, 2656, 3009, 3384, 3781, 4200, 4641, 5104, 5589, 6096, 6625, 7176, 7749, 8344, 8961, 9600, 10261, 10944, 11649, 12376, 13125, 13896, 14689, 15504, 16341 (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 parallel line from 1, in the direction 1, 69,..., in the square spiral whose vertices are the generalized 24-gonal numbers. - Omar E. Pol, Jul 18 2012 This is also a star dodecagonal number: a(n) = A051624(n) + 12*A000217(n-1). - Luciano Ancora, Mar 30 2015 REFERENCES Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189. E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6. LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 Index to sequences related to polygonal numbers Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 22*n+a(n-1)-21, with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010 G.f.: x*(1+21*x)/(1-x)^3. - Colin Barker, Jan 10 2012 a(22*a(n)+232*n+1) = a(22*a(n)+232*n) + a(22*n+1). - Vladimir Shevelev, Jan 24 2014 Product_{n>=2} (1 - 1/a(n)) = 11/12. - Amiram Eldar, Jan 22 2021 E.g.f.: exp(x)*(x + 11*x^2). - Nikolaos Pantelidis, Feb 05 2023 MAPLE A051876:=n->n*(11*n - 10); seq(A051876(n), n=0..50); # Wesley Ivan Hurt, Feb 25 2014 MATHEMATICA Table[n (11 n - 10), {n, 0, 50}] (* Wesley Ivan Hurt, Feb 25 2014 *) PROG (PARI) a(n)=n*(11*n-10) \\ Charles R Greathouse IV, Jul 19 2011 CROSSREFS Sequence in context: A087406 A319972 A304157 * A069174 A124717 A126378 Adjacent sequences: A051873 A051874 A051875 * A051877 A051878 A051879 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 15 1999 STATUS approved

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Last modified March 3 21:06 EST 2024. Contains 370517 sequences. (Running on oeis4.)