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 A286918 Total number of nodes summed over all lattice paths from (0,0) to (n,n) using steps {(k,0), (0,k) | 0
 1, 3, 21, 159, 1257, 10046, 81811, 674184, 5605141, 46920874, 394949193, 3339464105, 28343082002, 241324470723, 2060357315568, 17632454524499, 151211115930880, 1299121121946684, 11179500360964780, 96344672766997340, 831385476662968094, 7182777882757416692 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) ~ c * d^n / sqrt(n), where d = 8.84734830841870961487278801886633962039798... is the real root of the equation 4 + 4*d - 8*d^2 - 8*d^3 + d^4 = 0 and c = 0.43633259077568249345422000202799136319250347607927734138960545201547... - Vaclav Kotesovec, May 30 2017 MAPLE b:= proc(x, y) option remember; `if`(y>x or y<0, 0, `if`(x=0, [1\$2], add((p-> p+[0, p[1]])( b(x-j, y)+b(x, y-j)), j=1..4))) end: a:= n-> b(n\$2)[2]: seq(a(n), n=0..25); MATHEMATICA b[x_, y_] := b[x, y] = If[y > x || y < 0, {0, 0}, If[x == 0, {1, 1}, Sum[Function[p, p + {0, p[[1]]}][b[x-j, y] + b[x, y-j]], {j, 1, 4}]]]; a[n_] := b[n, n][[2]]; a /@ Range[0, 25] (* Jean-François Alcover, Dec 29 2020, after Alois P. Heinz *) CROSSREFS Cf. A175891. Sequence in context: A026333 A205773 A192364 * A358953 A189508 A074570 Adjacent sequences: A286915 A286916 A286917 * A286919 A286920 A286921 KEYWORD nonn AUTHOR Alois P. Heinz, May 17 2017 STATUS approved

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Last modified December 2 09:50 EST 2023. Contains 367517 sequences. (Running on oeis4.)