A128822 Number of solutions to x/3 + y/4 + z/6 < n with x,y,z>=1 .

2, 47, 206, 551, 1154, 2087, 3422, 5231, 7586, 10559, 14222, 18647, 23906, 30071, 37214, 45407, 54722, 65231, 77006, 90119, 104642, 120647, 138206, 157391, 178274, 200927, 225422, 251831, 280226, 310679, 343262, 378047, 415106, 454511, 496334

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 12*n^3-15*n^2+6*n-1.

G.f.: x*(2+39*x+30*x^2+x^3) / (x-1)^4. - R. J. Mathar, Apr 26 2015

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Jun 19 2025

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {2, 47, 206, 551}, 50] (* Harvey P. Dale, Jun 16 2018 *)

Crossrefs

Sequence in context: A153213 A355009 A304725 * A226420 A160922 A276509

Adjacent sequences: A128819 A128820 A128821 * A128823 A128824 A128825

Keyword

nonn,easy

Author

Philippe Deléham, Apr 11 2007

Status

approved