Number of ways n competitors can rank in a competition, allowing for the possibility of ties.| oeis.org
The On-Line Encyclopedia of Integer Sequences (OEIS)| oeis.org
OFFSET| oeis.org
Write 0, 1, 2, ... in a clockwise spiral; sequence gives numbers on one of 4 diagonals.| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
OFFSET| oeis.org
IMPORTANT:| oeis.org
Where record values of d(n) occur: d(n) > d(k) for all k < n.| oeis.org
D. E. Knuth writes: "Before Fibonacci wrote his work, the sequence F_{n} had already been discussed by Indian scholars, who had long been interested in rhythmic patterns that are formed from one-beat and two-beat notes. The number of such rhythms having n beats altogether is F_{n+1}; therefore both Gopāla (before 1135) and Hemachandra (c. 1150) mentioned the numbers 1, 2, 3, 5, 8, 13, 21, ... explicitly." (TAOCP Vol. 1, 2nd ed.) - Peter Luschny, Jan 11 2015| oeis.org