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 A123937 Triangle read by rows: T(x, y) = 0 if y > x, = 1 if y = 0, or = 2*Sum_{k >= 1, x-k^2 >= y} T(x-k^2, y-1) otherwise. The zeros are omitted from the sequence. 2
 1, 1, 2, 1, 2, 4, 1, 2, 4, 8, 1, 4, 4, 8, 16, 1, 4, 12, 8, 16, 32, 1, 4, 12, 32, 16, 32, 64, 1, 4, 12, 32, 80, 32, 64, 128, 1, 4, 16, 32, 80, 192, 64, 128, 256, 1, 6, 16, 56, 80, 192, 448, 128, 256, 512, 1, 6, 24, 56, 176, 192, 448, 1024, 256, 512, 1024 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Comments from R. J. Mathar, Oct 31 2006: This sequence provides the seeds for the construction of columns (vertical recurrence) of A122510 insofar as each row of A123937 provides two sides of auxiliary arrays b(.,.,.) from which a column of A122510 emerges as the third side: A122510(d,n)=b(0,d,n) [with an auxiliary, virtual A122510(0,n)=1]. Seeds to construct two sides of b(.,.,.): b(x,0,n)=A123937(n,x) for x<=n; b(n,y,n)=A123937(n,n) for y>=0. Recurrence within the b(.,.,.) : b(x,y,n)=b(x,y-1,n)+b(x+1,y-1,n) for x

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Last modified May 24 16:05 EDT 2024. Contains 372778 sequences. (Running on oeis4.)