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A002941 Arrays of dumbbells.
(Formerly M4396 N1852)
11
1, 7, 29, 94, 263, 667, 1577, 3538, 7622, 15900, 32314, 64274, 125561, 241569, 458715, 861242, 1601081, 2950693, 5396209, 9801012, 17692092, 31759800, 56727588, 100861716, 178585489, 314995915, 553650761, 969967510, 1694235803 (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.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

R. C. Grimson, Exact formulas for 2 x n arrays of dumbbells, J. Math. Phys., 15.2 (1974), 214-216. (Annotated scanned copy)

Index entries for linear recurrences with constant coefficients, signature (5,-7,-2,10,-2,-5,1,1).

FORMULA

G.f.: (1+x)^2/(1-x-x^2)^3/(1-x)^2.

a(n) = 2*a(n-1) - a(n-3) + A002940(n) + A002940(n-1).

MATHEMATICA

CoefficientList[(1+x)^2/(1-x-x^2)^3/(1-x)^2 + O[x]^30, x] (* Jean-Fran├žois Alcover, Jul 31 2018 *)

PROG

(Haskell)

a002941 n = a002941_list !! (n-1)

a002941_list = 1 : 7 : 29 : zipWith (+)

   (zipWith (-) (map (* 2) $ drop 2 a002941_list) a002941_list)

   (drop 2 $ zipWith (+) (tail a002940_list) a002940_list)

-- Reinhard Zumkeller, Jan 18 2014

(PARI) x='x+O('x^99); Vec((1+x)^2/(1-x-x^2)^3/(1-x)^2) \\ Altug Alkan, Jul 31 2018

CROSSREFS

Cf. A046741, A002940, A002889, A055608, A062123-A062127.

Sequence in context: A290901 A294843 A042609 * A193655 A227086 A102485

Adjacent sequences:  A002938 A002939 A002940 * A002942 A002943 A002944

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Henry Bottomley, Jun 02 2000

STATUS

approved

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)