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 A005996 G.f.: 2(1-x^3)/((1-x)^5*(1+x)^2). (Formerly M1609) 3
 2, 6, 16, 30, 54, 84, 128, 180, 250, 330, 432, 546, 686, 840, 1024, 1224, 1458, 1710, 2000, 2310, 2662, 3036, 3456, 3900, 4394, 4914, 5488, 6090, 6750, 7440, 8192, 8976, 9826, 10710, 11664, 12654, 13718 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is also the number of triples (w,x,y) having all terms in {0,...,n} and w 2. - Eric W. Weisstein, Mar 27 2018 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Enrique Pérez Herrero, Table of n, a(n) for n = 1..1000 S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), pp. 1917-1926. S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy) Eric Weisstein's World of Mathematics, Longest Path Problem Eric Weisstein's World of Mathematics, Web Graph Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 1, 2, -1). FORMULA a(n) = 2*(A006918(n) + A006918(n-1) + A006918(n-2)), n>1. - Ralf Stephan, Apr 26 2003 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6), with a(1)=2, a(2)=6, a(3)=16, a(4)=30, a(5)=54, a(6)=84. - Harvey P. Dale, Apr 08 2013 MATHEMATICA Table[(1/4)*(1 + n)*(-2 + 5*n + n^2 + 2*Ceiling[1/2 - n/2] - 4*Floor[n/2]), {n, 1, 200}] (* Enrique Pérez Herrero, Aug 03 2012 *) CoefficientList[Series[2 (1 - x^3)/((1 - x)^5 (1 + x)^2), {x, 0, 40}], x] (* Harvey P. Dale, Apr 08 2013 *) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {2, 6, 16, 30, 54, 84}, 40] (* Harvey P. Dale, Apr 08 2013 *) Table[(n + 1) (2 n (n + 2) + 1 - (-1)^n)/8, {n, 20}] (* Eric W. Weisstein, Mar 27 2018 *) CROSSREFS Essentially twice A034828. Sequence in context: A192532 A230853 A160620 * A192735 A171218 A032091 Adjacent sequences:  A005993 A005994 A005995 * A005997 A005998 A005999 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Aug 03 2012 STATUS approved

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Last modified October 21 06:25 EDT 2019. Contains 328292 sequences. (Running on oeis4.)