A055608 Arrays of dumbbells.

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

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<x>:=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