A033182 Number of pairs (p,q) such that 5*p + 6*q = n.

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, 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, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3

Offset: 0

Author

Michel Tixier (tixier(AT)dyadel.net)

Keywords

• nonn

Comments

Number of partitions of n into parts 5 and 6. - Seiichi Manyama, Jun 14 2017

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vincenzo Librandi)
• A. V. Kitaev and A. Vartanian, Algebroid Solutions of the Degenerate Third Painlevé Equation for Vanishing Formal Monodromy Parameter, arXiv:2304.05671 [math.CA], 2023. See p. 20.

Crossrefs

Cf. A033183.

Programs

Magma

[Floor(n/5)-Floor((n-1)/6): n in [0..100]]; // Vincenzo Librandi, Oct 13 2013

Mathematica

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 *)

Formula

a(n) = [ 5*n/6 ] + 1 + [ -4*n/5 ].

a(n) = floor(n/5) - floor((n-1)/6). - Mircea Merca, Oct 11 2013