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 A006191 Number of paths on square lattice. (Formerly M1490) 0
 1, 2, 5, 16, 54, 180, 595, 1964, 6485, 21418, 70740, 233640, 771661, 2548622, 8417525, 27801196, 91821114, 303264540, 1001614735, 3308108744, 10925940965, 36085931638, 119183735880, 393637139280, 1300095153721, 4293922600442 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES H. L. Abbott and D. Hanson, A lattice path problem, Ars Combin., 6 (1978), 163-178. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS H. L. Abbott and D. Hanson, A lattice path problem, Ars Combin., 6 (1978), 163-178. (Annotated scanned copy) FORMULA a(n) = 1 + Sum_{k=1..n-1} A006189(k). - Sean A. Irvine, Jan 20 2017 Conjectures from Colin Barker, Jan 20 2017: (Start) a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) + a(n-4) for n>4. G.f.: x*(1 - 2*x) / ((1 - x + x^2)*(1 - 3*x - x^2)). (End) MATHEMATICA LinearRecurrence[{4, -3, 2, 1}, {1, 2, 5, 16}, 30] (* Harvey P. Dale, Mar 22 2018 *) CROSSREFS Sequence in context: A100442 A081126 A018191 * A149959 A161941 A120899 Adjacent sequences:  A006188 A006189 A006190 * A006192 A006193 A006194 KEYWORD nonn,walk,changed AUTHOR EXTENSIONS Offset corrected and more terms from Sean A. Irvine, Jan 20 2017 STATUS approved

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Last modified March 24 15:46 EDT 2018. Contains 301205 sequences. (Running on oeis4.)