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A337560 Number of length four 1..n vectors that contain their harmonic mean.

%I A337560 #17 Feb 04 2023 18:21:17
%S A337560 1,2,3,28,29,78,79,104,105,154,155,252,253,254,351,376,377,426,427,
%T A337560 620,717,718,719,912,913,914,915,1084,1085,1374,1375,1400,1425,1426,
%U A337560 1619,1812,1813,1814,1839,2128,2129,2442,2443,2564,2829,2830,2831,3192,3193
%N A337560 Number of length four 1..n vectors that contain their harmonic mean.
%H A337560 Hywel Normington, <a href="https://github.com/Horep/Number-of-vectors-that-contain-their-average/blob/master/A337560.py">Python code</a>, 2020.
%F A337560 a(n) - a(n-1) = 1 (mod 12).
%e A337560 For n = 1, the a(1) = 1 solution is (1,1,1,1).
%e A337560 For n = 4, the a(4) = 28 solutions are (k,k,k,k) for k=1,2,3,4, the 12 permutations of (1,2,4,4) and the 12 permutations of (2,3,4,4).
%e A337560 For n = 40, the a(40) - a(39) = 289 new solutions are:
%e A337560   the 24 permutations of (4, 8, 10, 40),
%e A337560   the 12 permutations of (4, 10, 40, 40),
%e A337560   the 12 permutations of (5, 12, 40, 40),
%e A337560   the 24 permutations of (8, 10, 12, 40),
%e A337560   the 24 permutations of (8, 15, 20, 40),
%e A337560   the 12 permutations of (10, 16, 16, 40),
%e A337560   the 24 permutations of (10, 18, 24, 40),
%e A337560   the 12 permutations of (10, 20, 40, 40),
%e A337560   the 24 permutations of (12, 20, 24, 40),
%e A337560   the 24 permutations of (14, 24, 35, 40),
%e A337560   the 24 permutations of (15, 24, 30, 40),
%e A337560   the 12 permutations of (16, 16, 20, 40),
%e A337560   the 12 permutations of (20, 20, 24, 40),
%e A337560   the 12 permutations of (20, 30, 40, 40),
%e A337560   the 12 permutations of (24, 30, 30, 40),
%e A337560   the 12 permutations of (28, 35, 40, 40),
%e A337560   the 12 permutations of (30, 36, 40, 40),
%e A337560   and (40, 40, 40, 40).
%Y A337560 Cf. A248434, A337110, A337111, A337559.
%K A337560 nonn
%O A337560 1,2
%A A337560 _Hywel Normington_, Aug 31 2020
%E A337560 a(43)-a(49) from _Alois P. Heinz_, Feb 04 2023