A242926 a(n) = denominator of B(0,n), where B(n,n) = 0, B(n-1,n) = 1/n and otherwise B(m,n) = B(m-1,n+1) - B(m-1,n).

1, 1, 1, 2, 1, 6, 1, 4, 3, 5, 1, 4, 1, 7, 15, 8, 1, 18, 1, 10, 21, 11, 1, 24, 5, 13, 9, 14, 1, 30, 1, 16, 11, 17, 35, 12, 1, 19, 39, 20, 1, 42, 1, 22, 9, 23, 1, 48, 7, 25, 17, 26, 1, 54, 55, 28, 19, 29, 1, 20, 1

Offset: 0

Author

Paul Curtz, May 26 2014

Keywords

• nonn

Comments

The numerators are A189731(n).

B(0,n) = 0, 1, 1, 3/2, 2, 17/6, 4, 23/4, 25/3, 61/5, 18, 107/4, 40, 421/7, ...

is a super autosequence as defined in A242563.

The positive integers in B(0,n) give A064723(n). Corresponding rank: A006093(n+1). B(0,n) is linked to the primes A000040.

Divisor of B(0,n), n > 0: 1, 1, 1, 2, 2, 4, 5, ... = A172128(n+1).

Common (LCM) denominators for the antidiagonals: 1, 1, 1, 2, 2, 6, 6, 12, 12, ... = A139550(n+1)?.

1 = 1

1/2 + 3/2 = 2

1/3 + 5/6 + 17/6 = 4

1/4 + 7/12 + 7/4 + 23/4 = 25/3

etc.

The positive terms of the first bisection are the sum of the corresponding antidiagonal terms upon the 0's.

0 followed by A001610(n), i.e., 0, 0, 2, 3, 6, 10, 17, ... is an autosequence of the second kind.

Crossrefs

Cf. A000204, A175386, A001610, A189731, A139550, A242563.

Programs

Mathematica

Table[Denominator[(LucasL[n+1]-1)/(n+1)], {n, 0, 100}] (* Artur Jasinski, Nov 06 2022 *)

Formula

a(2n+1) = A175386(n).

a(n) = denominator(A001610(n)/(n+1)). [edited by Michel Marcus, Nov 14 2022]

a(n) = denominator((A000204(n+1) - 1)/(n+1)). - Artur Jasinski, Nov 06 2022

Extensions

a(24)-a(60) from Jean-François Alcover, May 26 2014