A290335 Number of representations of n as a sum of four terms of A020330 (including 0), where order matters.

1, 0, 0, 4, 0, 0, 6, 0, 0, 4, 4, 0, 1, 12, 0, 4, 12, 0, 12, 4, 6, 12, 0, 12, 4, 12, 6, 0, 24, 0, 10, 12, 0, 16, 0, 12, 10, 0, 12, 12, 13, 0, 12, 12, 0, 16, 12, 0, 16, 24, 6, 24, 12, 0, 32, 16, 12, 24, 24, 12, 25, 36, 0, 32, 36, 12, 40, 24, 12, 36, 36, 12, 34, 36, 12, 40, 36, 12, 30, 36, 12, 40, 36, 12, 52, 24, 12, 36, 24, 12, 34, 48, 6, 52, 36, 0, 54, 12, 12

Offset

0,4

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 = 24 there are four representations, which are the distinct permutations of [15,3,3,3].

Mathematica

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

Crossrefs

Cf. A020330, A261132, A290334, A298731.

Sequence in context: A021718 A193108 A212044 * A341795 A063730 A355945

Adjacent sequences: A290332 A290333 A290334 * A290336 A290337 A290338

Keyword

nonn,look

Author

Jeffrey Shallit, Jul 27 2017

Status

approved