bibkey: yanev2016a163617
authors: Velin Yanev
year: 2016
title: "OEIS A163617, a(2*n) = 2*a(n), a(2*n + 1) = 2*a(n) + 2 + (-1)^n, for all n in Z"
doi: null
url: https://oeis.org/A163617
claim: "A163617 %N: a(2*n) = 2*a(n), a(2*n + 1) = 2*a(n) + 2 + (-1)^n, for all n in Z. A163617 %F: Conjecture: a(n) = A003188(n) + (6*n + 1 - (-1)^n)/4. - _Velin Yanev_, Dec 17 2016. A003188 %N: Decimal equivalent of Gray code for n. A003188 %F: a(n) = n XOR floor(n/2), where XOR is the binary exclusive OR operator."
strata_touched:
  - D5/S1/Digit/Admissibility/GrayCodeBinaryRecurrenceClosedForm
license: citation-only
triage: anchor

OEIS A163617

The entry defines an integer-indexed recurrence and records Velin Yanev’s closed-form conjecture. The formal module proves the nonnegative-index half, initialized by a(0) = 0. It does not claim the negative-index half, which the entry relates to A163618.

The Gray-code term is OEIS A003188. Its entry names the decimal equivalent of the Gray code for n and gives the formula a(n) = n XOR floor(n/2), where XOR is binary exclusive OR. For nonnegative n, the parity-split correction used in the formal module equals (6*n + 1 - (-1)^n)/4 over the integers.

Verified locator

• URL: https://oeis.org/A163617
• Locator: FORMULA, “Conjecture: a(n) = A003188(n) + (6*n + 1 - (-1)^n)/4. - Velin Yanev, Dec 17 2016”