A339186 Total number of nonzero squares in the partitions of n into 2 parts.

0, 0, 2, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 5, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset

0,3

Links

Table of n, a(n) for n=0..91.

Index entries for sequences related to partitions

Formula

a(n) = A339184(n) + A339183(n).

Example

a(8) = 3; The partitions of 8 into two parts are (7,1), (6,2), (5,3) and (4,4). There are 3 total nonzero squares among the parts (namely 1, 4 and 4 ), so a(8) = 3.
a(9) = 2; The partitions of 9 into two parts are (8,1), (7,2), (6,3) and (5,4). Since 1 and 4 are the only nonzero squares among all parts, a(9) = 2.

Mathematica

Table[Sum[Floor[Sqrt[i]] - Floor[Sqrt[i - 1]] + Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]], {i, Floor[n/2]}], {n, 0, 100}]

Crossrefs

Cf. A339183 (number of smaller parts), A339184 (number of larger parts).

Sequence in context: A341771 A092335 A278912 * A302479 A029355 A029307

Adjacent sequences: A339183 A339184 A339185 * A339187 A339188 A339189

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Nov 26 2020

Status

approved