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 A308241 Total number of nodes summed over all lattice paths from (0,0) to (n,n) that consist of steps (h,v) with h, v prime or one. 3
 1, 2, 5, 18, 68, 244, 880, 3228, 11905, 43966, 162498, 600984, 2222776, 8218022, 30368708, 112162230, 414006377, 1527214022, 5630258676, 20744334800, 76387507859, 281129870088, 1034103899368, 3801934437930, 13971364199298, 51318841190524, 188420580871859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..600 Wikipedia, Counting lattice paths MAPLE b:= proc(x, y) option remember; `if`(y=0, [1\$2], (p-> p+[0, p[1]])( add(add(`if`((h=1 or isprime(h)) and (v=1 or isprime(v)), b(sort([x-h, y-v])[]), 0), v=1..y), h=1..x))) end: a:= n-> b(n\$2)[2]: seq(a(n), n=0..30); MATHEMATICA f[p_List] := p + {0, p[[1]]}; f[0] = 0; b[{x_, y_}] := b[{x, y}] = If[y == 0, {1, 1}, f[ Sum[Sum[If[(h == 1 || PrimeQ[h]) && (v == 1 || PrimeQ[v]), b[Sort@{x - h, y - v}], {0, 0}], {v, 1, y}], {h, 1, x}]]]; a[n_] := b[{n, n}][[2]]; a /@ Range[0, 30] (* Jean-François Alcover, Apr 05 2021, after Alois P. Heinz *) CROSSREFS Cf. A000040, A008578, A308240, A308274. Sequence in context: A150023 A150024 A150025 * A363061 A288910 A249062 Adjacent sequences: A308238 A308239 A308240 * A308242 A308243 A308244 KEYWORD nonn AUTHOR Alois P. Heinz, May 16 2019 STATUS approved

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Last modified December 6 01:58 EST 2023. Contains 367594 sequences. (Running on oeis4.)