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 A069190 Centered 24-gonal numbers. 19
 1, 25, 73, 145, 241, 361, 505, 673, 865, 1081, 1321, 1585, 1873, 2185, 2521, 2881, 3265, 3673, 4105, 4561, 5041, 5545, 6073, 6625, 7201, 7801, 8425, 9073, 9745, 10441, 11161, 11905, 12673, 13465, 14281, 15121, 15985, 16873, 17785, 18721, 19681, 20665, 21673 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sequence found by reading the line from 1, in the direction 1, 25,..., in the square spiral whose vertices are the generalized octagonal numbers A001082. Semi-axis opposite to A135453 in the same spiral. - Omar E. Pol, Sep 16 2011 LINKS Ivan Panchenko, Table of n, a(n) for n = 1..1000 E. Weisstein, Centered Polygonal Numbers Index entries for linear recurrences with constant coefficients, signature (3, -3, 1). FORMULA a(n) = 12*n^2 - 12*n + 1. a(n) = 24*n+a(n-1)-24 (with a(1)=1). - Vincenzo Librandi, Aug 08 2010 a(1)=1, a(2)=25, a(3)=73, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 17 2011 G.f.: x*(1+22*x+x^2)/(1-x)^3. - Harvey P. Dale, Jul 17 2011 Binomial transform of [1, 24, 24, 0, 0, 0,......] and Narayana transform (Cf. A001263) of [1, 24, 0, 0, 0...]. - Gary W. Adamson, Jul 26 2011 From Amiram Eldar, Jun 21 2020: (Start) Sum_{n>=1} 1/a(n) = Pi*tan(Pi/sqrt(6))/(4*sqrt(6)). Sum_{n>=1} a(n)/n! = 13*e - 1. Sum_{n>=1} (-1)^n * a(n)/n! = 13/e - 1. (End) EXAMPLE a(5) = 241 because 12*5^2 - 12*5 + 1 = 300 - 60 + 1 = 241. MATHEMATICA FoldList[#1 + #2 &, 1, 24 Range@ 45] (* Robert G. Wilson v *) Table[12n^2-12n+1, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 25, 73}, 50] (* Harvey P. Dale, Jul 17 2011 *) PROG (PARI) a(n)=12*n^2-12*n+1 \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. centered k-gonal numbers with k=3..25: A005448, A001844, A005891, A003215, A069099, A016754, A060544, A062786, A069125, A003154, A069126, A069127, A069128, A069129, A069130, A069131, A069132, A069133, A069178, A069173, A069174, A069190, A262221. Sequence in context: A255184 A235941 A337156 * A124718 A126379 A114553 Adjacent sequences:  A069187 A069188 A069189 * A069191 A069192 A069193 KEYWORD nonn,easy AUTHOR Terrel Trotter, Jr., Apr 10 2002 EXTENSIONS More terms from Harvey P. Dale, Jul 17 2011 STATUS approved

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Last modified November 26 07:49 EST 2020. Contains 338632 sequences. (Running on oeis4.)