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 A129703 Number of different walks generated by n steps that can only go in {east, southeast, southwest} directions on the 300-degree wedge in a 60-degree equilateral triangular lattice. 0
 1, 3, 6, 14, 36, 97, 268, 751, 2124, 6047, 17304, 49722, 143366, 414585, 1201918, 3492118, 10165780, 29643871, 86574832, 253188112, 741365050, 2173243129, 6377181826, 18730782253, 55062586342, 161995031227, 476941691178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n > 0, a(n)-1 is the sum of the n-th row of Motzkin's triangle (A026300). - Daniel Suteu, Feb 23 2018 LINKS FORMULA Recurrence: {a(3) = 14, a(4) = 36, a(1) = 3, a(2) = 6, a(0) = 1, (-3-3*n)*a(n)+(-6-2*n)*a(1+n)+(3+n)*a(n+2)+6+4*n}. G.f.: ((1/2)*i)*sqrt(t+1)/(t*sqrt(3*t-1))-(1/2)*(t+1)*(-1+2*t)/((t-1)*t). a(n) = 1 + Sum_{k=0..n} Sum_{t=0..floor(k/2)} binomial(n, 2*t + n - k) * (binomial(2*t + n - k, t) - binomial(2*t + n - k, t-1)), for n > 0. - Daniel Suteu, Feb 23 2018 EXAMPLE a(1) = 3 because all three directions are permissible from the origin; a(2) = 6 because all three directions are permissible following the southwestern step and the southwest as well as southeast steps are permissible following the southeastern step, but only the eastern step is permissible following one step east. CROSSREFS Sequence in context: A332362 A196479 A147772 * A001550 A197461 A100446 Adjacent sequences:  A129700 A129701 A129702 * A129704 A129705 A129706 KEYWORD nonn,walk AUTHOR Rebecca Xiaoxi Nie (rebecca.nie(AT)utoronto.ca), Jun 01 2007 STATUS approved

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Last modified February 26 01:41 EST 2020. Contains 332270 sequences. (Running on oeis4.)