bibkey: seidov2005a104863 authors: Zak Seidov; Ralf Stephan year: 2005 title: “OEIS A104863, a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=10, a(2)=30” doi: null url: https://oeis.org/A104863 claim: “a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=10, a(2)=30. For n>=17, a(n) = a(n-2) + a(n-4) + 1 (conjectured). If true then for m>5, a(2m+1) = 4F(m) + 25F(m+1) + 1 and a(2m+2) = 8F(m) + 30F(m+1) + 1 with F(n) = A000045(n). - Ralf Stephan, Nov 15 2010 Zak Seidov, Mar 28 2005” strata_touched:

• D5/S0/Certificates/StephanFloorSqrtRecurrenceRefutation license: citation-only triage: anchor

OEIS A104863

The NAME of A104863 states:

a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=10, a(2)=30.

The FORMULA conjecture is printed as:

For n>=17, a(n) = a(n-2) + a(n-4) + 1 (conjectured). If true then for m>5, a(2m+1) = 4F(m) + 25F(m+1) + 1 and a(2m+2) = 8F(m) + 30F(m+1) + 1 with F(n) = A000045(n). - Ralf Stephan, Nov 15 2010

The AUTHOR line is:

Zak Seidov, Mar 28 2005

The certified value at index 17 refutes only the literal universal conjecture. No corrected recurrence or exhaustive literature claim follows.

Verified locator

• URL: https://oeis.org/A104863
• NAME (verbatim): a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=10, a(2)=30.
• FORMULA conjecture line (verbatim): For n>=17, a(n) = a(n-2) + a(n-4) + 1 (conjectured). If true then for m>5, a(2m+1) = 4F(m) + 25F(m+1) + 1 and a(2m+2) = 8F(m) + 30F(m+1) + 1 with F(n) = A000045(n). - Ralf Stephan, Nov 15 2010
• AUTHOR (verbatim): Zak Seidov, Mar 28 2005