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 A051874 22-gonal numbers: a(n) = n*(10*n-9). 10
 0, 1, 22, 63, 124, 205, 306, 427, 568, 729, 910, 1111, 1332, 1573, 1834, 2115, 2416, 2737, 3078, 3439, 3820, 4221, 4642, 5083, 5544, 6025, 6526, 7047, 7588, 8149, 8730, 9331, 9952, 10593, 11254, 11935, 12636, 13357, 14098, 14859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sequence found by reading the line from 0, in the direction 0, 22,... and the parallel line from 1, in the direction 1, 63,..., in the square spiral whose vertices are the generalized 22-gonal numbers. - Omar E. Pol, Jul 18 2012 Also sequence found by reading the segment (0, 1) together with the line from 1, in the direction 1, 22,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 29 2012 This is also a star hendecagonal number: a(n) = A051682(n) + 11*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 Vincenzo Librandi, 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) = 2*a(n-1)-a(n-2)+20 with n>1, a(0)=0, a(1)=1. - Zerinvary Lajos, Feb 18 2008 a(n) = 20*n+a(n-1)-19 with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010 G.f.: x*(1+19*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011 a(20*a(n)+191*n+1) = a(20*a(n)+191*n) + a(20*n+1). - Vladimir Shevelev, Jan 24 2014 Product_{n>=2} (1 - 1/a(n)) = 10/11. - Amiram Eldar, Jan 22 2021 E.g.f.: exp(x)*(x + 10*x^2). - Nikolaos Pantelidis, Feb 05 2023 MAPLE a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+20 od: seq(a[n], n=0..39); # Zerinvary Lajos, Feb 18 2008 MATHEMATICA Table[n (10 n -9), {n, 0, 40}] (* Harvey P. Dale, Sep 19 2011 *) CoefficientList[Series[x (1 + 19 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *) PROG (PARI) a(n)=n*(10*n-9) \\ Charles R Greathouse IV, Jan 24 2014 CROSSREFS Sequence in context: A216299 A255431 A221595 * A140390 A069178 A081929 Adjacent sequences: A051871 A051872 A051873 * A051875 A051876 A051877 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 15 1999 STATUS approved

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Last modified September 22 16:46 EDT 2023. Contains 365531 sequences. (Running on oeis4.)