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%I #6 Jan 01 2023 09:48:32
%S 1,1,2,2,2,3,2,2,2,4,2,2,4,2,4,2,4,2,2,4,4,2,2,4,2,2,4,4,2,3,4,4,4,4,
%T 2,4,2,8,2,2,4,2,2,2,6,2,2,4,4,2,2,4,2,4,8,4,2,4,6,2,4,4,2,2,2,8,4,4,
%U 4,2,4,4,4,2,4,4,2,4,4,4,2,2,8,4,4,2,4
%N For n >= 0, let S be the sequence of numbers m such that (m^2 - 2*n^2 + 1)/2 is a square. Then a(n) is the number k such that S(j) = 6*S(j-k) - S(j-2k) for all j for which S(j-2k) is defined.
%F a(0) = 1; for n >= 1, a(n) = A000005(2*n^2 - 1).
%e For n = 0, {S(j)} = A002315 (the NSW numbers), which satisfies S(j) = 6*S(j-1) - S(j-2), so a(0) = 1.
%e For n = 1, {S(j)} = A001541, which also satisfies S(j) = 6*S(j-1) - S(j-2), so a(1) = 1.
%e For n = 2, {S(j)} = A077443, which satisfies S(j) = 6*S(j-2) - S(j-4), so a(2) = 2.
%e For n = 5, {S(j)} = A106525, which satisfies S(j) = 6*S(j-3) - S(j-6), so a(5) = 3.
%Y Cf. A000005, A002315, A001541, A077443, A077242, A106525.
%K nonn
%O 0,3
%A _Jon E. Schoenfield_, Dec 31 2022
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