The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A127620 Number of walks from (0,0) to (n,n) in the region 0 <= x-y <= 6 with the steps (1,0), (0, 1), (2,0) and (0,2). 3
 1, 1, 5, 22, 117, 654, 3843, 22882, 137443, 827998, 4995443, 30155494, 182083275, 1099560942, 6640309323, 40101959542, 242184540139, 1462610652718, 8833070227499, 53345145429670, 322164911643723, 1945636121710110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..21. 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 (6, 5, -24, -28, -6, 8). FORMULA G.f.: (1 - 5x - 6x^2 + 11x^3 + 12x^4 - 4x^5)/(1 - 6x - 5x^2 + 24x^3 + 28x^4 + 6x^5 - 8x^6). [corrected by Jean-François Alcover, Apr 02 2019] 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 b[n_, k_] := Boole[n >= 0 && k >= 0 && 0 <= n-k <= 6]; T[0, 0] = T[1, 1] = 1; T[n_, k_] /; b[n, k] == 1 := T[n, k] = b[n-1, k]* T[n-1, k] + b[n-2, k]*T[n-2, k] + b[n, k-1]*T[n, k-1] + b[n, k-2]*T[n, k-2]; T[_, _] = 0; a[n_] := T[n, n]; Table[a[n], {n, 0, 21}] (* or: *) LinearRecurrence[{6, 5, -24, -28, -6, 8}, {1, 1, 5, 22, 117, 654}, 22] (* Jean-François Alcover, Apr 02 2019 *) CROSSREFS Cf. A000108, A046717, A122951, A127617, A127618, A127619. Sequence in context: A005033 A127618 A127619 * A122951 A331836 A184181 Adjacent sequences: A127617 A127618 A127619 * A127621 A127622 A127623 KEYWORD nonn,easy,walk AUTHOR Arvind Ayyer, Jan 20 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 31 11:21 EDT 2023. Contains 363066 sequences. (Running on oeis4.)