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%I #19 Sep 08 2022 08:45:44
%S 1,2,6,18,54,160,476,1416,4212,12528,37264,110840,329688,980640,
%T 2916864,8676064,25806512,76760160,228319200,679123872,2020019488,
%U 6008445440,17871816000,53158809600,158118181056,470314504192,1398926621696,4161036233088
%N Expansion of 1/(1 - 2*x - 2*x^2 - 2*x^3 - 2*x^4).
%C 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.
%C 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
%D Arthur Benjamin and Jennifer Quinn, Proofs that Really Count, Mathematical Association of America, 2003, p. 36.
%H G. C. Greubel, <a href="/A160175/b160175.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,2,2).
%F a(n) = 2*(a(n-1) + a(n-2) + a(n-3) + a(n-4)).
%t 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}]
%t LinearRecurrence[{2,2,2,2},{1,2,6,18},30] (* _Harvey P. Dale_, Oct 27 2013 *)
%t 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 *)
%o (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
%o (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
%Y Cf. A077835, A002605, A000079.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, May 03 2009, May 06 2009
%E More terms from _Harvey P. Dale_, Oct 27 2013
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