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%I #12 Sep 08 2022 08:45:01
%S 1,13,92,473,1982,7191,23431,70234,196941,522939,1327002,3240917,
%T 7660538,17602967,39466363,86593478,186399956,394478234,822229746,
%U 1690521204,3433033150,6893852746,13702694284,26982983126,52680389239
%N Arrays of dumbbells.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
%D R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216.
%D R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099.
%H Reinhard Zumkeller, <a href="/A055608/b055608.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (9,-31,44,4,-84,66,46,-74,-4,36,-4,-9,1,1).
%F G.f.: (1+x)^4/((1-x)^4*(1-x-x^2)^5).
%F a(n) = 2*a(n-1) - a(n-3) + A002889(n) + A002889(n-1).
%t CoefficientList[Series[(1+x)^4/((1-x)^4*(1-x-x^2)^5), {x,0,30}], x] (* _G. C. Greubel_, Jan 31 2019 *)
%o (Haskell)
%o a055608 n = a055608_list !! (n-1)
%o a055608_list = 1 : 13 : 92 : zipWith (+)
%o (zipWith (-) (map (* 2) $ drop 2 a055608_list) a055608_list)
%o (drop 2 $ zipWith (+) (tail a002889_list) a002889_list)
%o -- _Reinhard Zumkeller_, Jan 18 2014
%o (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
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)^4/((1-x)^4*(1-x-x^2)^5) )); // _G. C. Greubel_, Jan 31 2019
%o (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
%Y Cf. A002940, A002941, A002889, A046741.
%Y Cf. A062123-A062127.
%K easy,nonn
%O 1,2
%A _Henry Bottomley_, Jun 02 2000
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