Number of ordered ways of writing n as the sum of 3 triangular numbers

Arrangements, combinations and permutations, probability, ...
Cot-O-Bus
Posts: 6
Joined: Thu Sep 27, 2018 9:18 am

Number of ordered ways of writing n as the sum of 3 triangular numbers

Hello colleagues,

I've implemented strait forward algorithm for case 3 according to page 6 On the representation of integers as sums of triangular numbers

But it produces wrong results for n = { 3, 9, 12, 18, 21, 30, 34, 39, 45, 48, 57, 59, 63, 66, 67, 75, 84, 93 }. Can somebody give me a hint what i miss from this document?

Code: Select all

R3(n)={
my( s=0 );
if( n%4==1, for( r=1, floor(n/4), s+=kronecker( r, n ) ); s*=24 );
if( n%4==3, for( r=1, floor(n/2), s+=kronecker( r, n ) ); s*=8 );
s
}

s3(n)={
my( s=0 );
fordiv( 8*n+3, d,
if( issquare( d ),
s+=R3( (8*n+3)/d )
)
);
s/8
}