A351742 Number of partitions of 2n into n parts of size 1, 5, 10 or 25.

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

Offset

0,25

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,0,0,0,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,-1,0,0,0,0,-1,0,0,0,1).

Formula

G.f.: -1/(x^37-x^33-x^28+x^24-x^13+x^9+x^4-1).

a(n) = A351725(2n,n).

Example

a(0) = 1: [].
a(4) = 1: [{5}^1,{1}^3].
a(24) = 2: [{5}^6,{1}^18], [{25}^1,{1}^23].
a(36) = 3: [{5}^9,{1}^27], [{10}^4,{1}^32], [{25}^1,{5}^3,{1}^32].

Crossrefs

Cf. A351725.

Sequence in context: A371244 A353835 A033183 * A090677 A161097 A105240

Adjacent sequences: A351739 A351740 A351741 * A351743 A351744 A351745

Keyword

nonn,easy

Author

Alois P. Heinz, Feb 17 2022

Status

approved