A359438 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.
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, 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, 4, 2, 4, 4, 4, 2, 4, 4, 2, 4, 4, 4, 2, 2, 8, 4, 4, 2, 4
Offset: 0
Keywords
Examples
For n = 0, {S(j)} = A002315 (the NSW numbers), which satisfies S(j) = 6*S(j-1) - S(j-2), so a(0) = 1.
For n = 1, {S(j)} = A001541, which also satisfies S(j) = 6*S(j-1) - S(j-2), so a(1) = 1.
For n = 2, {S(j)} = A077443, which satisfies S(j) = 6*S(j-2) - S(j-4), so a(2) = 2.
For n = 5, {S(j)} = A106525, which satisfies S(j) = 6*S(j-3) - S(j-6), so a(5) = 3.
Formula
a(0) = 1; for n >= 1, a(n) = A000005(2*n^2 - 1).