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.

1, 14, 128, 1378, 13932, 144300, 1480376, 15245184, 156756896, 1612836306, 16589928984, 170664508406, 1755592926518, 18059752212038, 185779058543356, 1911097952732140, 19659326724616886, 202234169412143472, 2080368880383488938, 21400612097499844490, 220146623069820835050

Offset: 0

Author

Bryan T. Ek, Mar 19 2018

Keywords

• nonn
• walk

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]}.

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A300998, A301380, A301381.

Programs

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);

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).