This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002889 M4715 N2016 #35 Sep 08 2022 08:44:31
%S A002889 1,10,56,234,815,2504,7018,18336,45328,107160,244198,539656,1161987,
%T A002889 2446906,5054440,10266850,20549117,40595568,79271188,153190480,
%U A002889 293278496,556737696,1048772300,1961855408,3646420325,6737649754
%N A002889 Arrays of dumbbells.
%D A002889 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(2.3.14).
%D A002889 R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15 (1974), 214-216.
%D A002889 R. B. McQuistan and S. J. Lichtman, Exact recursion relation for 2 x N arrays of dumbbells, J. Math. Phys., 11 (1970), 3095-3099.
%D A002889 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002889 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002889 Reinhard Zumkeller, <a href="/A002889/b002889.txt">Table of n, a(n) for n = 1..1000</a>
%H A002889 R. C. Grimson, <a href="/A002889/a002889.pdf">Exact formulas for 2 x n arrays of dumbbells</a>, J. Math. Phys., 15.2 (1974), 214-216. (Annotated scanned copy)
%H A002889 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,11,19,-29,-3,21,-3,-7,1,1).
%F A002889 a(n) = 2*a(n-1) - a(n-3) + A002941(n) + A002941(n-1).
%F A002889 G.f.: (1+x)^3/((1-x)^3*(1-x-x^2)^4).
%t A002889 CoefficientList[(1+x)^3/((1-x)^3*(1-x-x^2)^4) + O[x]^30, x] (* _Jean-François Alcover_, Jul 31 2018 *)
%t A002889 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 *)
%o A002889 (Haskell)
%o A002889 a002889 n = a002889_list !! (n-1)
%o A002889 a002889_list = 1 : 10 : 56 : zipWith (+)
%o A002889 (zipWith (-) (map (* 2) $ drop 2 a002889_list) a002889_list)
%o A002889 (drop 2 $ zipWith (+) (tail a002941_list) a002941_list)
%o A002889 -- _Reinhard Zumkeller_, Jan 18 2014
%o A002889 (PARI) x='x+O('x^30); Vec((1+x)^3/((1-x)^3*(1-x-x^2)^4)) \\ _Altug Alkan_, Jul 31 2018
%o A002889 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)^3/((1-x)^3*(1-x-x^2)^4) )); // _G. C. Greubel_, Jan 31 2019
%o A002889 (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
%Y A002889 Cf. A046741, A002940, A002941.
%Y A002889 Cf. A055608, A062123-A062127.
%K A002889 nonn,easy
%O A002889 1,2
%A A002889 _N. J. A. Sloane_
%E A002889 More terms from _Henry Bottomley_, Jun 02 2000