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A340760
Number of partitions of n into 4 parts whose largest 3 parts have the same parity.
0
0, 0, 0, 0, 1, 0, 1, 1, 3, 1, 4, 3, 7, 4, 9, 7, 14, 9, 17, 14, 24, 17, 29, 24, 38, 29, 45, 38, 57, 45, 66, 57, 81, 66, 93, 81, 111, 93, 126, 111, 148, 126, 166, 148, 192, 166, 214, 192, 244, 214, 270, 244, 305, 270, 335, 305, 375, 335, 410, 375, 455, 410, 495, 455, 546, 495
OFFSET
0,9
FORMULA
a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} [(j mod 2) = (i mod 2) = ((n-i-j-k) mod 2)], where [ ] is the (generalized) Iverson bracket.
G.f.: x^4/((x^2+x+1)*(x^2+1)^2*(x+1)^3*(x-1)^4). - Alois P. Heinz, Jan 19 2021
MATHEMATICA
Table[Sum[Sum[Sum[KroneckerDelta[Mod[i, 2], Mod[j, 2], Mod[n - i - j - k, 2]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]
CROSSREFS
Sequence in context: A209613 A264596 A262214 * A035626 A082587 A364670
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 19 2021
STATUS
approved