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%I M1490 #30 Mar 21 2021 17:28:11
%S 1,2,5,16,54,180,595,1964,6485,21418,70740,233640,771661,2548622,
%T 8417525,27801196,91821114,303264540,1001614735,3308108744,
%U 10925940965,36085931638,119183735880,393637139280,1300095153721,4293922600442
%N Number of paths on square lattice.
%D H. L. Abbott and D. Hanson, A lattice path problem, Ars Combin., 6 (1978), 163-178.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Michael De Vlieger, <a href="/A006191/b006191.txt">Table of n, a(n) for n = 1..1928</a>
%H H. L. Abbott and D. Hanson, <a href="/A006189/a006189.pdf">A lattice path problem</a>, Ars Combin., 6 (1978), 163-178. (Annotated scanned copy)
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,2,1).
%F a(n) = 1 + Sum_{k=1..n-1} A006189(k). - _Sean A. Irvine_, Jan 20 2017
%F From _Colin Barker_, Jan 20 2017: (Start)
%F a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) + a(n-4) for n>4.
%F G.f.: x*(1 - 2*x) / ((1 - x + x^2)*(1 - 3*x - x^2)).
%F (End)
%t LinearRecurrence[{4,-3,2,1},{1,2,5,16},30] (* _Harvey P. Dale_, Mar 22 2018 *)
%K nonn,walk,easy
%O 1,2
%A _N. J. A. Sloane_
%E Offset corrected and more terms from _Sean A. Irvine_, Jan 20 2017
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