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A055608 Arrays of dumbbells.

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