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

0,3

Links

Table of n, a(n) for n=0..86.

Formula

a(0) = 1; for n >= 1, a(n) = A000005(2*n^2 - 1).

Example

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.

Crossrefs

Cf. A000005, A002315, A001541, A077443, A077242, A106525.

Sequence in context: A301375 A325273 A352541 * A279408 A135592 A022912

Adjacent sequences: A359435 A359436 A359437 * A359439 A359440 A359441

Keyword

nonn

Author

Jon E. Schoenfield, Dec 31 2022

Status

approved