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%I M5352 #47 Sep 10 2022 07:34:44
%S 76,288,700,1376,2380,3776,5628,8000,10956,14560,18876,23968,29900,
%T 36736,44540,53376,63308,74400,86716,100320,115276,131648,149500,
%U 168896,189900,212576,236988,263200,291276,321280,353276,387328,423500,461856,502460,545376
%N Number of walks on cubic lattice.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Richard K. Guy, <a href="/A005555/a005555.pdf">Letter to N. J. A. Sloane, May 1990</a>.
%H Richard K. Guy, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/GUY/catwalks.html">Catwalks, sandsteps and Pascal pyramids</a>, J. Integer Sequences, Vol. 3 (2000), Article 00.1.6 (see Figure 7).
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: 4*(19-4*x+x^2)/(x-1)^4. - _Simon Plouffe_ in his 1992 dissertation
%F a(n) = 4(n+1)(n+3)(8n+19)/3.
%F Sum_{n>=0} 1/a(n) = 499/1936 + (6*log(1+sqrt(2))*sqrt(2) - 3*(sqrt(2)-1)*Pi - 24*log(2))/55. - _Amiram Eldar_, Sep 10 2022
%t a[n_] := 4 (n + 1) (n + 3) (8 n + 19)/3; Array[a, 30, 0] (* _Amiram Eldar_, Sep 10 2022 *)
%o (PARI) vector(40, n, n--; 4*(n+1)*(n+3)*(8*n+19)/3) \\ _Michel Marcus_, Oct 13 2014
%K nonn,walk,easy
%O 0,1
%A _N. J. A. Sloane_
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