OFFSET
1,2
FORMULA
Conjectures from Colin Barker, Apr 07 2018: (Start)
G.f.: x^2*(5 + 3*x + 5*x^2 + 3*x^3 + 2*x^4) / ((1 - x)^3*(1 + x)^2*(1 + x^2)).
a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7) for n>7.
(End)
EXAMPLE
Count the even parts for a(n) (n > 0).
13 + 1 + 1
12 + 2 + 1
11 + 3 + 1
10 + 4 + 1
9 + 5 + 1
8 + 6 + 1
7 + 7 + 1
10 + 1 + 1 11 + 2 + 2
9 + 2 + 1 10 + 3 + 2
8 + 3 + 1 9 + 4 + 2
7 + 4 + 1 8 + 5 + 2
6 + 5 + 1 7 + 6 + 2
7 + 1 + 1 8 + 2 + 2 9 + 3 + 3
6 + 2 + 1 7 + 3 + 2 8 + 4 + 3
5 + 3 + 1 6 + 4 + 2 7 + 5 + 3
4 + 4 + 1 5 + 5 + 2 6 + 6 + 3
4 + 1 + 1 5 + 2 + 2 6 + 3 + 3 7 + 4 + 4
3 + 2 + 1 4 + 3 + 2 5 + 4 + 3 6 + 5 + 4
1 + 1 + 1 2 + 2 + 2 3 + 3 + 3 4 + 4 + 4 5 + 5 + 5
3(1) 3(2) 3(3) 3(4) 3(5) .. 3n
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0 5 8 18 24 .. a(n)
MATHEMATICA
Table[Count[Flatten[IntegerPartitions[3 n, {3}]], _?EvenQ], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 07 2018
STATUS
approved