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There's something not displaying properly in my computer's rendition of the formula for the number of solutions. Thanks for the answer. My purely experimental version of the formula is Ceiling[p/8] with no exceptions as far as I carried the computation.
To Felipe Voloch. I like this answer very much. If I've understood, the idea is this: For every partition of n into three squares, there is a partition of n+49 into 4 squares one of which is 7-squared, and vice-versa. Therefore if we find that there are more partitions of n+49 into 4 parts than there are partitions of n into 3 parts, some of these partitions into 4 parts must not contain 49.
@YvesCornulier By my definition 1,2,1,3,3,0,0,0,0,.... is not unimodal. It has two local maxima:2 and 3. The sequence 1,2,3,3,0,0,0,... is unimodal by my definition. It has a single maximum: 3, although 3 appears more than once, its appearances come for successive values of f. The sequence 1,2,3,2,3,... would not meet my definition of unimodal. Although the only maximum is 3, its two appearances are separated by the value 2. I haven't looked at the Wikipedia definition, but I'd guess that it deals with functions on a continuous domain. Here we have values for f only at integers.
