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
Examples
For n = 24 there are four representations, which are the distinct permutations of [15,3,3,3].
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.
Programs
-
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 *)