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%I #21 Jun 27 2022 11:08:24
%S 1,1,3,4,7,8,13,14,20,22,29,31,40,42,52,55,66,69,82,85,99,103,118,122,
%T 139,143,161,166,185,190,211,216,238,244,267,273,298,304,330,337,364,
%U 371,400,407,437,445,476,484,517,525,559,568,603,612,649,658,696,706,745,755
%N Simon Plouffe's conjectured extension of sequence A008368.
%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1,-1,-2,0,1).
%F G.f.: (1-x^5)/((1-x)*(1-x^2)^2*(1-x^3)).
%F Euler transform of length 5 sequence [ 1, 2, 1, 0, -1]. - _Michael Somos_, May 22 2014
%F a(-3 - n) = a(n). - _Michael Somos_, May 22 2014
%F a(2*n + 2) - a(2*n) = A032793(n + 2). a(2*n + 3) - a(2*n + 1) = A042706(n + 2). - _Michael Somos_, May 22 2014
%e G.f. = 1 + x + 3*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 13*x^6 + 14*x^7 + 20*x^8 + ...
%t CoefficientList[Series[(1-x^5)/((1-x)*(1-x^2)^2*(1-x^3)), {x, 0, 59}], x] (* _Georg Fischer_, Oct 13 2020 *)
%o (PARI) {a(n) = if( n%2, (n + 1) * (5*n + 7) + 8 * (n%6 == 3), (n + 2) * (5*n + 8) + 8 * (n%6 == 0) ) / 24}; /* _Michael Somos_, May 22 2014 */
%o (PARI) {a(n) = if( n<0, n = -3 - n); polcoeff( (1 - x^5) / ((1 - x) * (1 - x^2)^2 * (1 - x^3)) + x * O(x^n), n)}; /* _Michael Somos_, May 22 2014 */
%Y Cf. A032793, A042706.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_ and _J. H. Conway_
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