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A301379 Number of close American football games: number of ways for the game to have n scoring plays and never be separated by more than one score after each play. 3
1, 14, 128, 1378, 13932, 144300, 1480376, 15245184, 156756896, 1612836306, 16589928984, 170664508406, 1755592926518, 18059752212038, 185779058543356, 1911097952732140, 19659326724616886, 202234169412143472, 2080368880383488938, 21400612097499844490, 220146623069820835050 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Each play (counting untimed downs as part of the previous play) can score at most 8 points for one team.

The same as counting walks of x-length n from the origin bounded above by y=8, below by y=-8, and using the steps {[1,8],..,[1,2],[1,-2],..,[1,-8]}.

LINKS

Table of n, a(n) for n=0..20.

Bryan Ek, Lattice Walk Enumeration, arXiv:1803.10920 [math.CO], 2018.

Bryan Ek, Unimodal Polynomials and Lattice Walk Enumeration with Experimental Mathematics, arXiv:1804.05933 [math.CO], 2018.

FORMULA

G.f.: (1+10*t+13*t^2-37*t^3-40*t^4+28*t^5+26*t^6-2*t^7)/(1-4*t-59*t^2-77*t^3+170*t^4+234*t^5-92*t^6-142*t^7-4*t^8+6*t^9).

EXAMPLE

For n=1, any step is valid. For n=2, any walk with steps of opposite direction is valid while [[1,3],[1,6]] is an example of an invalid walk.

MAPLE

taylor((1+10*t+13*t^2-37*t^3-40*t^4+28*t^5+26*t^6-2*t^7)/(1-4*t-59*t^2-77*t^3+170*t^4+234*t^5-92*t^6-142*t^7-4*t^8+6*t^9), t=0, N);

CROSSREFS

Cf. A300998, A301380, A301381.

Sequence in context: A166794 A229386 A208047 * A222571 A038841 A240189

Adjacent sequences:  A301376 A301377 A301378 * A301380 A301381 A301382

KEYWORD

nonn,walk

AUTHOR

Bryan T. Ek, Mar 19 2018

STATUS

approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)