A160175 Expansion of 1/(1 - 2*x - 2*x^2 - 2*x^3 - 2*x^4).

1, 2, 6, 18, 54, 160, 476, 1416, 4212, 12528, 37264, 110840, 329688, 980640, 2916864, 8676064, 25806512, 76760160, 228319200, 679123872, 2020019488, 6008445440, 17871816000, 53158809600, 158118181056, 470314504192, 1398926621696, 4161036233088

Offset

0,2

Comments

a(n) is the number of ways two opposing baseball teams could score a combined total of n runs (tallying the score just prior to each "batter up!") considering the order of the scoring as important. Equivalently, a(n) is the number of 2-colored tilings of an n-board with tiles of length at most 4.

a(n) is the number of compositions (ordered partitions) of n into parts <= 4 with 2 sorts of each part. - Joerg Arndt, Aug 06 2019

References

Arthur Benjamin and Jennifer Quinn, Proofs that Really Count, Mathematical Association of America, 2003, p. 36.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,2,2).

Formula

a(n) = 2*(a(n-1) + a(n-2) + a(n-3) + a(n-4)).

Mathematica

RecurrenceTable[{a[n] == 2(a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4]), a[0] == 1, a[1] == 2, a[2] == 6, a[3] == 18}, a, {n, 0, 20}]
LinearRecurrence[{2, 2, 2, 2}, {1, 2, 6, 18}, 30] (* Harvey P. Dale, Oct 27 2013 *)
CoefficientList[Series[1/(1-2*x-2*x^2-2*x^3-2*x^4), {x, 0, 50}], x] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(1/(1-2*x-2*x^2-2*x^3-2*x^4)) \\ G. C. Greubel, Sep 24 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-2*x-2*x^2-2*x^3-2*x^4))); // G. C. Greubel, Sep 24 2018

Crossrefs

Cf. A077835, A002605, A000079.

Sequence in context: A072850 A254941 A182899 * A072852 A072853 A179344

Adjacent sequences: A160172 A160173 A160174 * A160176 A160177 A160178

Keyword

nonn

Author

Geoffrey Critzer, May 03 2009, May 06 2009

Extensions

More terms from Harvey P. Dale, Oct 27 2013

Status

approved