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

0,31

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.

Formula

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

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

Prog

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

Crossrefs

Cf. A033183.

Sequence in context: A097587 A001179 A001876 * A053797 A254011 A361919

Adjacent sequences: A033179 A033180 A033181 * A033183 A033184 A033185

Keyword

nonn

Author

Michel Tixier (tixier(AT)dyadel.net)

Status

approved