

A290335


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


5



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
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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. 18:118:14; arXiv preprint, arXiv:1710.04247 [math.NT], 20172018.


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 A131431
Adjacent sequences: A290332 A290333 A290334 * A290336 A290337 A290338


KEYWORD

nonn,look


AUTHOR

Jeffrey Shallit, Jul 27 2017


STATUS

approved



