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 A002889 Arrays of dumbbells. (Formerly M4715 N2016) 11
 1, 10, 56, 234, 815, 2504, 7018, 18336, 45328, 107160, 244198, 539656, 1161987, 2446906, 5054440, 10266850, 20549117, 40595568, 79271188, 153190480, 293278496, 556737696, 1048772300, 1961855408, 3646420325, 6737649754 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14). R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216. R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15.2 (1974), 214-216. (Annotated scanned copy) Index entries for linear recurrences with constant coefficients, signature (7,-17,11,19,-29,-3,21,-3,-7,1,1). FORMULA a(n) = 2*a(n-1) - a(n-3) + A002941(n) + A002941(n-1). G.f.: (1+x)^3/((1-x)^3*(1-x-x^2)^4). MATHEMATICA CoefficientList[(1+x)^3/((1-x)^3*(1-x-x^2)^4) + O[x]^30, x] (* Jean-François Alcover, Jul 31 2018 *) LinearRecurrence[{7, -17, 11, 19, -29, -3, 21, -3, -7, 1, 1}, {1, 10, 56, 234, 815, 2504, 7018, 18336, 45328, 107160, 244198}, 30] (* Harvey P. Dale, Jul 25 2021 *) PROG (Haskell) a002889 n = a002889_list !! (n-1) a002889_list = 1 : 10 : 56 : zipWith (+) (zipWith (-) (map (* 2) \$ drop 2 a002889_list) a002889_list) (drop 2 \$ zipWith (+) (tail a002941_list) a002941_list) -- Reinhard Zumkeller, Jan 18 2014 (PARI) x='x+O('x^30); Vec((1+x)^3/((1-x)^3*(1-x-x^2)^4)) \\ Altug Alkan, Jul 31 2018 (Magma) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)^3/((1-x)^3*(1-x-x^2)^4) )); // G. C. Greubel, Jan 31 2019 (Sage) ((1+x)^3/((1-x)^3*(1-x-x^2)^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019 CROSSREFS Cf. A046741, A002940, A002941. Cf. A055608, A062123-A062127. Sequence in context: A320756 A053309 A035040 * A055911 A087076 A014483 Adjacent sequences: A002886 A002887 A002888 * A002890 A002891 A002892 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Henry Bottomley, Jun 02 2000 STATUS approved

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Last modified January 30 07:42 EST 2023. Contains 359942 sequences. (Running on oeis4.)