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 A127618 Number of walks from (0,0) to (n,n) in the region 0 <= x-y <= 4 with the steps (1,0), (0, 1), (2,0) and (0,2). 3
 1, 1, 5, 22, 117, 590, 3018, 15378, 78440, 399992, 2039852, 10402480, 53049048, 270531368, 1379614800, 7035549312, 35878823312, 182969359520, 933079279328, 4758375627808, 24266039468160, 123748253080832, 631072497876672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Arvind Ayyer and Doron Zeilberger, The Number of [Old-Time] Basketball games with Final Score n:n where the Home Team was never losing but also never ahead by more than w Points, arXiv:math/0610734 [math.CO], 2006-2007. Index entries for linear recurrences with constant coefficients, signature (4,6,-2). FORMULA G.f.: (1-3x-5x^2-2x^3+x^4)/(1-4x-6x^2+2x^3). EXAMPLE a(2)=5 because we can reach (2,2) in the following ways: (0,0),(1,0),(1,1),(2,1),(2,2) (0,0),(2,0),(2,2) (0,0),(1,0),(2,0),(2,2) (0,0),(2,0),(2,1),(2,2) (0,0),(1,0),(2,0),(2,1),(2,2) MATHEMATICA Join[{1, 1}, LinearRecurrence[{4, 6, -2}, {5, 22, 117}, 21]] (* Jean-François Alcover, Dec 10 2018 *) b[n_, k_] := Boole[n >= 0 && k >= 0 && 0 <= n-k <= 4]; T[0, 0] = T[1, 1] = 1; T[n_, k_] /; b[n, k] == 1 := T[n, k] = b[n-2, k]* T[n-2, k] + b[n-1, k]*T[n-1, k] + b[n, k-2]*T[n, k-2] + b[n, k-1]*T[n, k-1]; T[_, _] = 0; a[n_] := T[n, n]; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Apr 03 2019 *) CROSSREFS Cf. A000108, A046717, A122951, A127617, A127619, A127620. Sequence in context: A213167 A355398 A005033 * A127619 A127620 A122951 Adjacent sequences: A127615 A127616 A127617 * A127619 A127620 A127621 KEYWORD nonn,easy,walk AUTHOR Arvind Ayyer, Jan 20 2007 STATUS approved

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Last modified March 25 04:11 EDT 2023. Contains 361511 sequences. (Running on oeis4.)