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%I #27 Apr 14 2023 13:55:40
%S 1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,2,1,1,1,
%T 1,2,2,1,1,1,2,2,2,1,1,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,3,3,2,
%U 2,2,3,3,3,2,2,3,3,3,3,2,3,3,3,3,3,3,3
%N Number of pairs (p,q) such that 5*p + 6*q = n.
%C Number of partitions of n into parts 5 and 6. - _Seiichi Manyama_, Jun 14 2017
%H Seiichi Manyama, <a href="/A033182/b033182.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Vincenzo Librandi)
%H A. V. Kitaev and A. Vartanian, <a href="https://arxiv.org/abs/2304.05671">Algebroid Solutions of the Degenerate Third Painlevé Equation for Vanishing Formal Monodromy Parameter</a>, arXiv:2304.05671 [math.CA], 2023. See p. 20.
%F a(n) = [ 5*n/6 ] + 1 + [ -4*n/5 ].
%F a(n) = floor(n/5) - floor((n-1)/6). - _Mircea Merca_, Oct 11 2013
%t nn = 86; t = Table[0, {nn}]; Do[m = 5*p + 6*q; If[0 < m <= nn, t[[m]]++], {p, 0, nn/5}, {q, 0, nn/6}]; Join[{1}, t] (* _T. D. Noe_, Oct 07 2013 *)
%o (Magma) [Floor(n/5)-Floor((n-1)/6): n in [0..100]]; // _Vincenzo Librandi_, Oct 13 2013
%Y Cf. A033183.
%K nonn
%O 0,31
%A Michel Tixier (tixier(AT)dyadel.net)
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