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 A143689 a(n) = (3*n^2-n+2)/2. 6
 1, 2, 6, 13, 23, 36, 52, 71, 93, 118, 146, 177, 211, 248, 288, 331, 377, 426, 478, 533, 591, 652, 716, 783, 853, 926, 1002, 1081, 1163, 1248, 1336, 1427, 1521, 1618, 1718, 1821, 1927, 2036, 2148, 2263, 2381, 2502, 2626, 2753, 2883, 3016, 3152, 3291 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equals left border of triangle A033292. Equals binomial transform of [1, 1, 3, 0, 0, 0,...]. A242357(a(n)) = 1. - Reinhard Zumkeller, May 11 2014 LINKS D Bevan, D Levin, P Nugent, J Pantone, L Pudwell, Pattern avoidance in forests of binary shrubs, arXiv preprint arXiv:1510:08036, 2015 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = A000326(n+1) - 3*n. (A000326 are the pentagonal numbers). a(n) = (3*n^2-n+2)/2 = A027599(n+1)/2. - R. J. Mathar, Sep 03 2008 a(n) = a(n-1)+3*n-2 (with a(0)=1) - Vincenzo Librandi, Nov 25 2010 a(n) = 2*a(n-1)-a(n-2)+3. O.g.f.: (1-x+3*x^2)/((1-x)^3). - Eric Werley, Jun 27 2011 a(n) = A104249(-n). - Bruno Berselli, Jul 08 2015 MATHEMATICA Table[(3n^2-n+2)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 2, 6}, 50] (* Harvey P. Dale, May 05 2014 *) PROG (Haskell) a143689 n = n*(3*n-1) `div` 2 + 1 -- Reinhard Zumkeller, May 11 2014 (PARI) a(n)=(3*n^2-n+2)/2 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS a(n) = A000326(n+1) - 3n. Third column of A107111. Cf. A033292, A104249. Sequence in context: A258603 A064960 A293503 * A180773 A011891 A184533 Adjacent sequences:  A143686 A143687 A143688 * A143690 A143691 A143692 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Aug 29 2008 EXTENSIONS Corrected index of A000326 in definition, formula and example. - R. J. Mathar, Sep 03 2008 STATUS approved

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