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
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, May 03 2009, May 06 2009
EXTENSIONS
More terms from Harvey P. Dale, Oct 27 2013
STATUS
approved