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 A055608 Arrays of dumbbells. 9
 1, 13, 92, 473, 1982, 7191, 23431, 70234, 196941, 522939, 1327002, 3240917, 7660538, 17602967, 39466363, 86593478, 186399956, 394478234, 822229746, 1690521204, 3433033150, 6893852746, 13702694284, 26982983126, 52680389239 (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. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (9,-31,44,4,-84,66,46,-74,-4,36,-4,-9,1,1). FORMULA G.f.: (1+x)^4/((1-x)^4*(1-x-x^2)^5). a(n) = 2*a(n-1) - a(n-3) + A002889(n) + A002889(n-1). MATHEMATICA CoefficientList[Series[(1+x)^4/((1-x)^4*(1-x-x^2)^5), {x, 0, 30}], x] (* G. C. Greubel, Jan 31 2019 *) PROG (Haskell) a055608 n = a055608_list !! (n-1) a055608_list = 1 : 13 : 92 : zipWith (+) (zipWith (-) (map (* 2) \$ drop 2 a055608_list) a055608_list) (drop 2 \$ zipWith (+) (tail a002889_list) a002889_list) -- Reinhard Zumkeller, Jan 18 2014 (PARI) my(x='x+O('x^30)); Vec((1+x)^4/((1-x)^4*(1-x-x^2)^5)) \\ G. C. Greubel, Jan 31 2019 (Magma) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)^4/((1-x)^4*(1-x-x^2)^5) )); // G. C. Greubel, Jan 31 2019 (Sage) ((1+x)^4/((1-x)^4*(1-x-x^2)^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019 CROSSREFS Cf. A002940, A002941, A002889, A046741. Cf. A062123-A062127. Sequence in context: A300779 A275918 A027670 * A038742 A282709 A005414 Adjacent sequences: A055605 A055606 A055607 * A055609 A055610 A055611 KEYWORD easy,nonn AUTHOR Henry Bottomley, Jun 02 2000 STATUS approved

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Last modified April 16 08:27 EDT 2024. Contains 371698 sequences. (Running on oeis4.)