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

Author

Alois P. Heinz, Feb 17 2022

Keywords

• nonn
• easy

Examples

			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].
		

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).

Crossrefs

Cf. A351725.

Formula

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

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