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Denominators of irregular triangle of fractions arising from a problem of projecting into Hilbert space.
1

%I #15 Mar 20 2023 13:06:39

%S 1,2,1,4,4,8,1,16,8,8,32,16,16,1,64,32,16,16,128,64,64,32,1,256,128,

%T 32,32,64,32,512,256,256,128,128,1,1024,512,256,16,64,128,64,2048,

%U 1024,1024,512,128,256,256,1,4096,2048,128,512,1024,256,128,128,8192,4096,4096,2048,2048,512,512,512

%N Denominators of irregular triangle of fractions arising from a problem of projecting into Hilbert space.

%H H. H. Bauschke and R. M. Corless, <a href="https://www.researchgate.net/publication/322200645_MapleTech_Volume_4_no_1_Spring_1997">Analyzing a Projection Method with Maple</a>, MapleTech Journal, 4:1 (1997), 2-7.

%e Triangle begins:

%e [0],

%e [1/2],

%e [0,1/4],

%e [1/4,1/8],

%e [0,3/16,1/8],

%e [1/8,3/32,1/16,1/16],

%e [0,7/64,5/32,1/16],

%e [1/16,7/128,5/64,7/64,1/32],

%e [0,15/256,17/128,3/32,1/32,1/64],

%e [1/32,15/512,17/256,29/256,9/128,3/128],

%e [0,31/1024,49/512,23/256,1/16,3/64,1/128],

%e ...

%o (PARI) tabfd(nn) = my(m = htabl(nn), v = vector(nn, n, apply(denominator, Vec(m[n,], len(m[n,],n))))); for (n=1, #v, for (k=1, #v[n], print1(v[n][k], ", "))); \\ uses htabl and len from A345441 \\ _Michel Marcus_, Mar 20 2023

%Y Cf. A345441 (numerators).

%K nonn,frac,tabf

%O 1,2

%A _N. J. A. Sloane_, Jun 27 2021

%E More terms from _Michel Marcus_, Mar 20 2023