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 A192136 a(n) = (5*n^2-3*n+2)/2 3
 1, 2, 8, 19, 35, 56, 82, 113, 149, 190, 236, 287, 343, 404, 470, 541, 617, 698, 784, 875, 971, 1072, 1178, 1289, 1405, 1526, 1652, 1783, 1919, 2060, 2206, 2357, 2513, 2674, 2840, 3011, 3187, 3368, 3554, 3745, 3941, 4142, 4348, 4559, 4775, 4996, 5222, 5453 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of [1,1,5,0,0,0,0,0,....] [Johannes W. Meijer, Jul 07 2011] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = (5*n^2-3*n+2)/2 a(n) = 2*a(n-1)-a(n-2)+5 a(n) = a(n-1)+5*n-4 a(n) = 5*C(n+2, 2)-9*n-4 a(n) = A000217(n+1)-A000217(n)+5*A000217(n-1); triangular numbers [Johannes W. Meijer, Jul 07 2011] O.g.f.: (1-x+5*x^2)/((1-x)^3) MATHEMATICA Table[(5n^2-3n+2)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 2, 8}, 50] (* Harvey P. Dale, Aug 08 2016 *) PROG (MAGMA) A192136:=func< n | (5*n^2-3*n+2)/2 >; [ A192136(n): n in [0..50] ]; // Klaus Brockhaus, Jun 27 2011 (PARI) a(n)=n*(5*n-3)/2+1 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A000124, A002522, A143689, A130883, A000217, A006137, A140063, A140064. Sequence in context: A109071 A196134 A256321 * A031327 A193389 A030504 Adjacent sequences:  A192133 A192134 A192135 * A192137 A192138 A192139 KEYWORD nonn,easy AUTHOR Eric Werley, Jun 24 2011 STATUS approved

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