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 A005562 Number of walks on square lattice. (Formerly M3974) 5
 1, 5, 35, 140, 720, 2700, 12375, 45375, 196625, 715715, 3006003, 10930920, 45048640, 164105760, 668144880, 2441298600, 9859090500, 36149998500, 145173803500, 534239596880, 2136958387520, 7892175863000, 31479019635375, 116657543354625, 464342770607625, 1726402608669375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 4..1000 R. K. Guy, Letter to N. J. A. Sloane, May 1990 R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6, w_n'(4) FORMULA a(n) = C(n+5, ceiling(n/2))*C(n+4, floor(n/2)) - C(n+5, ceiling((n-1)/2))*C(n+4, floor((n-1)/2)). - Paul D. Hanna, Apr 16 2004 Conjecture: (n-3)*(n-4)*(2*n+1)*(n+7)*(n+6)*a(n) - 4*n*(n+1)*(2*n^2+4*n+51)*a(n-1) - 16*n^2*(n-1)*(2*n+3)*(n+1)*a(n-2) = 0. - R. J. Mathar, Apr 02 2017 MAPLE wnprime := proc(n, y) local k; if type(n-y, 'even') then k := (n-y)/2 ; binomial(n+1, k)*(binomial(n, k)-binomial(n, k-1)) ; else k := (n-y-1)/2 ; binomial(n+1, k)*binomial(n, k+1)-binomial(n+1, k+1)*binomial(n, k-1) ; end if; end proc: A005562 := proc(n) wnprime(n, 4) ; end proc: seq(A005562(n), n=4..30) ; # R. J. Mathar, Apr 02 2017 MATHEMATICA Table[Binomial[n+5, Ceiling[n/2]] Binomial[n+4, Floor[n/2]]-Binomial[n+5, Ceiling[(n-1)/2]] Binomial[n+4, Floor[(n-1)/2]], {n, 0, 30}] (* Vincenzo Librandi, Apr 03 2017 *) PROG (PARI) {a(n)=binomial(n+5, ceil(n/2))*binomial(n+4, floor(n/2)) - binomial(n+5, ceil((n-1)/2))*binomial(n+4, floor((n-1)/2))} (Magma) [Binomial(n+5, Ceiling(n/2))*Binomial(n+4, Floor(n/2)) - Binomial(n+5, Ceiling((n-1)/2))*Binomial(n+4, Floor((n-1)/2)): n in [0..30]]; // Vincenzo Librandi, Apr 03 2017 CROSSREFS Cf. A005558, A005559, A005560, A005561, A093768. Sequence in context: A096743 A026697 A000910 * A097872 A184707 A124793 Adjacent sequences: A005559 A005560 A005561 * A005563 A005564 A005565 KEYWORD nonn,walk AUTHOR STATUS approved

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Last modified February 5 14:24 EST 2023. Contains 360086 sequences. (Running on oeis4.)