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 A277424 Total number of nodes summed over all self-avoiding planar walks starting at (0,0), ending at (n,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1). 4
 1, 5, 39, 379, 4457, 61503, 974107, 17412317, 346662981, 7605810685, 182298744203, 4738700778123, 132767583248917, 3988244997744743, 127859570155253607, 4357113615504651565, 157266354405499307369, 5993377455733610208885, 240479249123008267155343 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 FORMULA From Vaclav Kotesovec, Oct 14 2016: (Start) Recurrence: (n^3 + n^2 - 6*n + 1)*a(n) = (4*n^4 + 6*n^3 - 28*n^2 + 3*n + 4)*a(n-1) - (4*n^5 + 2*n^4 - 42*n^3 + 50*n^2 - 13)*a(n-2) - (n-2)*(4*n^4 + 8*n^3 - 34*n^2 - n + 16)*a(n-3) - (n-3)*(n-2)*(n^3 + 4*n^2 - n - 3)*a(n-4). a(n) ~ sqrt(Pi) * 2^(n+3/2) * n^(n+11/4) / (3 * Gamma(1/4) * exp(n+1/4)). (End) MAPLE b:= proc(x, y, t) option remember; `if`(x<0 or y<0, 0,       `if`(x=0 and y=0, [1\$2], (p-> p+ [0, p[1]])(        b(x-1, y, 0)+ b(x, y-1, 0)+ b(x-1, y-1, 0)+       `if`(t<>2, b(x+1, y-1, 1), 0)+       `if`(t<>1, b(x-1, y+1, 2), 0))))     end: a:= n-> b(n, 0\$2)[2]: seq(a(n), n=0..25); MATHEMATICA b[x_, y_, t_] := b[x, y, t] = If[x < 0 || y < 0, 0, If[x == 0 && y == 0, {1, 1}, Function[p, p + {0, p[[1]]}][b[x - 1, y, 0] + b[x, y - 1, 0] + b[x - 1, y - 1, 0] + If[t != 2, b[x + 1, y - 1, 1], 0] + If[t != 1, b[x - 1, y + 1, 2], 0]]]]; a[n_] := b[n, 0, 0][[2]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jun 19 2017, translated from Maple *) CROSSREFS Cf. A277358, A284231, A285673. Sequence in context: A266456 A247772 A129763 * A182954 A215506 A316654 Adjacent sequences:  A277421 A277422 A277423 * A277425 A277426 A277427 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 14 2016 STATUS approved

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Last modified October 15 14:04 EDT 2018. Contains 316236 sequences. (Running on oeis4.)