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 A045947 Triangles in open triangular matchstick arrangement (triangle minus one side) of side n. 10
 0, 0, 2, 7, 17, 33, 57, 90, 134, 190, 260, 345, 447, 567, 707, 868, 1052, 1260, 1494, 1755, 2045, 2365, 2717, 3102, 3522, 3978, 4472, 5005, 5579, 6195, 6855, 7560, 8312, 9112, 9962, 10863, 11817, 12825, 13889, 15010, 16190, 17430, 18732, 20097, 21527 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (3, -2, -2, 3, -1). FORMULA G.f.: (2*x^2+x^3)/((1-x)^3*(1-x^2)). - Michael Somos a(n) = (1/16)*(2*n*(2*n^2+n-2)+(-1)^n-1). - Bruno Berselli, Aug 29 2011 a(2*n) = A000447(n)+A002412(n); a(2*n+1) = A051895(n). - J. M. Bergot, Apr 12 2018 MATHEMATICA LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, 2, 7, 17}, 45] (* Jean-François Alcover, Dec 12 2016 *) PROG (PARI) a(n)=(4*n^3+2*n^2-4*n)\16 (MAGMA) [Floor((4*n^3+2*n^2-4*n)/16): n in [0..50]]; // Vincenzo Librandi, Aug 29 2011 CROSSREFS First differences of A082289. Sequence in context: A166381 A083723 A294866 * A145066 A014148 A070070 Adjacent sequences:  A045944 A045945 A045946 * A045948 A045949 A045950 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified December 13 15:03 EST 2018. Contains 318086 sequences. (Running on oeis4.)