OFFSET
0,6
COMMENTS
Conjecturally the same as A230059 (apart from the offset). - R. J. Mathar, Jan 14 2021
LINKS
FORMULA
a(n) = Sum_{k=1..floor(n/3)} Sum_i=k..floor((n-k)/2)} (1 - [k = i = n-i-k]), where [ ] is the (generalized) Iverson bracket.
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1 - [k = i] * [2*i = n-k] * [2*k = n-i]), where [ ] is the Iverson bracket.
From Alois P. Heinz, Jan 07 2021: (Start)
G.f.: x^4*(x^2-x-1)/((x+1)*(x^2+x+1)*(x-1)^3).
a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6), n>6. (End)
a(n) = A036410(n-1)-1. - Hugo Pfoertner, Jan 09 2021
72*a(n) = -16*A099837(n+3) -9*(-1)^n +6*n^2 -31. - R. J. Mathar, Jun 09 2022
EXAMPLE
a(6) = 2; [4,1,1], [3,2,1] ( [2,2,2] not counted ),
a(7) = 4; [5,1,1], [4,2,1], [3,3,1], [3,2,2],
a(8) = 5; [6,1,1], [5,2,1], [4,3,1], [4,2,2], [3,3,2],
a(9) = 6; [7,1,1], [6,2,1], [5,3,1], [4,4,1], [5,2,2], [4,3,2] ( [3,3,3] not counted ).
MATHEMATICA
Table[Sum[Sum[(1 - KroneckerDelta[i, k, n - i - k]), {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 0, 80}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 07 2021
STATUS
approved