A340761 Number of partitions of n into 4 parts whose 'middle' two parts have the same parity.

0, 0, 0, 0, 1, 1, 1, 2, 4, 4, 5, 7, 10, 11, 13, 16, 21, 23, 26, 31, 38, 41, 46, 53, 62, 67, 74, 83, 95, 102, 111, 123, 138, 147, 159, 174, 192, 204, 219, 237, 259, 274, 292, 314, 340, 358, 380, 406, 436, 458, 484, 514, 549, 575, 605, 640, 680, 710, 745, 785, 830, 865, 905, 950, 1001

Offset

0,8

Links

Table of n, a(n) for n=0..64.

Index entries for sequences related to partitions

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)], where [ ] is the Iverson bracket.

Mathematica

Table[Sum[Sum[Sum[KroneckerDelta[Mod[i, 2], Mod[j, 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: A256984 A111138 A349462 * A035625 A219875 A132128

Adjacent sequences: A340758 A340759 A340760 * A340762 A340763 A340764

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 19 2021

Status

approved