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%I #4 Jul 25 2024 14:06:42
%S 0,1,1,2,3,4,6,7,9,12,12,14,18,18,24,24,26,29,36,36,36,48,48,49,52,54,
%T 59,72,72,72,72,78,96,96,96,98,104,104,109,118,118,144,144,144,144,
%U 144,150,156,192,192,192,192,194,196,208,208,210,218,222,236,236
%N a(n) = a[n/r] + a[n/r^2] + a[n/r^3] + ... , where a(0) = 0, a(1) = 1, r = 3/2, and [ ] = floor.
%C Conjecture: Let d(n) = a(n+1) - a(n) for n >= 0. Then d(n) = 1 for infinitely many n, and (d(n)) is unbounded.
%t a[0] = 0; a[1] = 1;
%t a[n_] := a[n] = Sum[a[Floor[n/(3/2)^k]], {k, 1, n}]
%t Table[a[n], {n, 0, 400}]
%Y Cf. A000045, A373095, A373096.
%K nonn
%O 0,4
%A _Clark Kimberling_, Jul 22 2024
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