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%I M5038 #68 Sep 10 2022 07:34:49
%S 17,50,99,164,245,342,455,584,729,890,1067,1260,1469,1694,1935,2192,
%T 2465,2754,3059,3380,3717,4070,4439,4824,5225,5642,6075,6524,6989,
%U 7470,7967,8480,9009,9554,10115,10692,11285
%N Number of walks on cubic lattice.
%C Partial sums of A158057.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Jeremy Gardiner, <a href="/A005570/b005570.txt">Table of n, a(n) for n = 1..999</a>
%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_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 8*n^2 + 9*n.
%F G.f.: (17-x)/(1-x)^3. _Simon Plouffe_ in his 1992 dissertation.
%F a(n) = 16 * A000217(n) + n. - _Jon Perry_, Nov 05 2014
%F Sum_{n>=1} 1/a(n) = 80/81 +Psi(1/8)/9+gamma/9 = 0.11973.. see A001620 and A250129. - _R. J. Mathar_, May 30 2022
%F Sum_{n>=1} 1/a(n) = 80/81 - (sqrt(2)+1)*Pi/18 - log(1+sqrt(2))*sqrt(2)/9 -4*log(2)/9. - _Amiram Eldar_, Sep 10 2022
%t CoefficientList[Series[(17 - x) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 05 2014 *)
%o (PARI) Vec((17-x)/(1-x)^3 + O(x^50)) \\ _Michel Marcus_, Nov 05 2014
%o (Magma) [8*n^2 + 9*n : n in [1..40]]; // _Vincenzo Librandi_, Nov 05 2014
%Y Cf. A000217, A001620, A158057, A250129.
%K nonn,walk,easy
%O 1,1
%A _N. J. A. Sloane_
%E Formula and more terms from _Jeffrey Shallit_, Aug 15 1995
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