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 A033537 a(n) = n*(2*n+5). 24
 0, 7, 18, 33, 52, 75, 102, 133, 168, 207, 250, 297, 348, 403, 462, 525, 592, 663, 738, 817, 900, 987, 1078, 1173, 1272, 1375, 1482, 1593, 1708, 1827, 1950, 2077, 2208, 2343, 2482, 2625, 2772, 2923, 3078, 3237, 3400, 3567, 3738, 3913, 4092, 4275, 4462, 4653, 4848, 5047, 5250, 5457, 5668 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Permutations avoiding 12-3 that contain the pattern 32-1 exactly once. a(n) = A014107(n) + 8*n^2; A100035(a(n)) = 3 for n>1. - Reinhard Zumkeller, Oct 31 2004 If Y is a 3-subset of an (2n+1)-set X then, for n>=1, a(n-1) is the number of (2n-1)-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 T. Mansour, Restricted permutations by patterns of type 2-1, arXiv:math/0202219 [math.CO], 2002. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = a(n-1) + 4*n + 3 (with a(0)=0). - Vincenzo Librandi, Nov 17 2010 From L. Edson Jeffery, Oct 14 2012: (Start) G.f.: x*(7-3*x)/(1-x)^3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=7, a(2)=18. (End) E.g.f.: x*(7 + 2*x)*exp(x). - G. C. Greubel, Jul 15 2017 From Amiram Eldar, Feb 06 2022: (Start) Sum_{n>=1} 1/a(n) = 46/75 - 2*log(2)/5. Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/10 + log(2)/5 - 26/75. (End) MAPLE seq(n*(2*n+5), n=0..60); # G. C. Greubel, Oct 14 2019 MATHEMATICA Table[n*(2*n+5), {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *) LinearRecurrence[{3, -3, 1}, {0, 7, 18}, 60] (* Harvey P. Dale, Nov 19 2021 *) PROG (PARI) a(n)=n*(2*n+5) \\ Charles R Greathouse IV, Jun 17 2017 (Magma) [n*(2*n+5): n in [0..60]]; // G. C. Greubel, Oct 14 2019 (Sage) [n*(2*n+5) for n in (0..60)] # G. C. Greubel, Oct 14 2019 (GAP) List([0..60], n-> n*(2*n+5) ); # G. C. Greubel, Oct 14 2019 CROSSREFS Cf. A100036, A100037, A100038, A100039. Sequence in context: A103572 A049532 A156619 * A352741 A225286 A000566 Adjacent sequences: A033534 A033535 A033536 * A033538 A033539 A033540 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 2 10:13 EST 2023. Contains 360011 sequences. (Running on oeis4.)