A145102 a(0) = a(1) = 1. a(n+1) = floor(n*a(n)/a(n-1)), for n >= 1.

1, 1, 1, 2, 6, 12, 10, 5, 3, 4, 12, 30, 27, 10, 4, 5, 18, 57, 53, 16, 5, 6, 25, 91, 83, 21, 6, 7, 31, 124, 116, 28, 7, 8, 37, 157, 148, 33, 8, 9, 43, 191, 182, 40, 9, 9, 45, 230, 240, 50, 10, 10, 51, 265, 275, 56, 11, 11, 57, 300, 310, 62, 12, 12, 63, 336, 346, 67, 12, 12, 69, 402

Offset: 0

Author

Leroy Quet, Oct 01 2008

Keywords

• nonn
• easy

Comments

At n = 62 the sequence settles down and becomes quasi-periodic with a 6-loop. - Ctibor O. Zizka, Feb 21 2025

Links

• Michel Marcus, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-5,6,-5,4,-3,2,-1,0,1,-2,3,-4,5,-6,5,-4,3,-2,1).

Crossrefs

Cf. A145103.

Programs

PARI

{print1(a=1, ",", b=1, ","); for(n=2, 71, print1(c=floor((n-1)*b/a), ","); a=b; b=c)} \\ Klaus Brockhaus, Oct 02 2008

Formula

From Ctibor O. Zizka, Feb 21 2025: (Start)

For n >= 62,

a(n) = n/6 + floor((n - 2)*(n - 3)/12) - 1 if n mod 6 = 0,

a(n) = n if n mod 6 = 1,

a(n) = 12 if n mod 6 = 2 or 3,

a(n) = n - 1 if n mod 6 = 4,

a(n) = floor((n - 1)*(n - 2)/12) if n mod 6 = 5. (End)

Extensions

More terms from Klaus Brockhaus and R. J. Mathar, Oct 02 2008