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 A002941 Arrays of dumbbells. (Formerly M4396 N1852) 12
 1, 7, 29, 94, 263, 667, 1577, 3538, 7622, 15900, 32314, 64274, 125561, 241569, 458715, 861242, 1601081, 2950693, 5396209, 9801012, 17692092, 31759800, 56727588, 100861716, 178585489, 314995915, 553650761, 969967510, 1694235803 (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 (5,-7,-2,10,-2,-5,1,1). FORMULA G.f.: (1+x)^2/((1-x-x^2)^3*(1-x)^2). a(n) = 2*a(n-1) - a(n-3) + A002940(n) + A002940(n-1). MATHEMATICA CoefficientList[(1+x)^2/((1-x-x^2)^3*(1-x)^2) + O[x]^30, x] (* Jean-François Alcover, Jul 31 2018 *) PROG (Haskell) a002941 n = a002941_list !! (n-1) a002941_list = 1 : 7 : 29 : zipWith (+)    (zipWith (-) (map (* 2) \$ drop 2 a002941_list) a002941_list)    (drop 2 \$ zipWith (+) (tail a002940_list) a002940_list) -- Reinhard Zumkeller, Jan 18 2014 (PARI) x='x+O('x^30); Vec((1+x)^2/((1-x-x^2)^3*(1-x)^2)) \\ Altug Alkan, Jul 31 2018 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)^2/((1-x-x^2)^3*(1-x)^2) )); // G. C. Greubel, Jan 31 2019 (Sage) ((1+x)^2/((1-x-x^2)^3*(1-x)^2)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019 CROSSREFS Cf. A046741, A002940, A002889, A055608, A062123-A062127. Sequence in context: A290901 A294843 A042609 * A193655 A227086 A102485 Adjacent sequences:  A002938 A002939 A002940 * A002942 A002943 A002944 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Henry Bottomley, Jun 02 2000 STATUS approved

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Last modified April 17 13:31 EDT 2021. Contains 343063 sequences. (Running on oeis4.)