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

0,31

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.

Example

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

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 *)

Crossrefs

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

Sequence in context: A080884 A354452 A362450 * A321102 A368199 A091392

Adjacent sequences: A298728 A298729 A298730 * A298732 A298733 A298734

Keyword

nonn

Author

Jeffrey Shallit, Jan 25 2018

Status

approved