A298731 Number of distinct representations of n as a sum of four terms of A020330 (including 0), where order does not matter.

1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 0, 1, 1, 0, 4, 1, 0, 2, 1, 1, 2, 1, 0, 3, 2, 1, 2, 1, 1, 3, 2, 0, 3, 2, 1, 4, 1, 1, 3, 2, 1, 3, 2, 1, 4, 2, 1, 3, 2, 1, 3, 2, 1, 4, 2, 1, 3, 1, 1, 4, 2, 1, 4, 2, 0, 4, 1, 1, 4, 2, 1, 3, 3, 0, 4, 1

Offset: 0

Author

Jeffrey Shallit, Jan 25 2018

Keywords

• nonn

Examples

			For n = 45, the a(45) = 4 solutions are 45 = 15+15+15 = 36+3+3+3 = 15+10+10+10.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Parthasarathy Madhusudan, Dirk Nowotka, Aayush Rajasekaran and Jeffrey Shallit, Lagrange's Theorem for Binary Squares, in: I. Potapov, P. Spirakis and J. Worrell (eds.), 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Schloss Dagstuhl, 2018, pp. 18:1-18:14; arXiv preprint, arXiv:1710.04247 [math.NT], 2017-2018.

Crossrefs

Cf. A020330, A290334, A290335 (which is the same sequence where order matters).

Programs

Mathematica

v = Table[k + k * 2^Floor[Log2[k] + 1], {k, 0, 8}]; a[n_] := Length @ IntegerPartitions[n, {4}, v]; Table[a[n], {n, 0, v[[-1]]}] (* Amiram Eldar, Apr 09 2021 *)