A376132 First differences of A376131.

1, 1, 4, 1, 4, 1, 11, 1, 4, 1, 11, 1, 4, 1, 26, 1, 4, 1, 11, 1, 4, 1, 26, 1, 4, 1, 11, 1, 4, 1, 57, 1, 4, 1, 11, 1, 4, 1, 26, 1, 4, 1, 11, 1, 4, 1, 57, 1, 4, 1, 11, 1, 4, 1, 26, 1, 4, 1, 11, 1, 4, 1, 120, 1, 4, 1, 11, 1, 4, 1, 26, 1, 4, 1, 11, 1, 4, 1, 57, 1, 4, 1, 11, 1, 4, 1, 26, 1

Offset

1,3

Comments

The sequence consists of Eulerian numbers from A000295.

The total number of fires for 2n and 2n-1 chips is the same, this is why the interesting increase is 2.

Links

Table of n, a(n) for n=1..88.

Dillan Agrawal, Selena Ge, Jate Greene, Tanya Khovanova, Dohun Kim, Rajarshi Mandal, Tanish Parida, Anirudh Pulugurtha, Gordon Redwine, Soham Samanta, and Albert Xu, Chip-Firing on Infinite k-ary Trees, arXiv:2501.06675 [math.CO], 2025. See p. 17.

Ryota Inagaki, Tanya Khovanova, and Austin Luo, On Chip-Firing on Undirected Binary Trees, Ann. Comb. (2025). See p. 24.

Wikipedia, Chip-firing game.

Formula

a(n) = A000295(A376116(n+1) - A376116(n) + 1).

Maple

b:= n-> (l-> add(((i-2)*2^(i-1)+1)*(l[i]+1), i=2..nops(l)-1))(Bits[Split](2*n+1)):
a:= n-> b(n+1)-b(n):
seq(a(n), n=1..88);  # Alois P. Heinz, Sep 12 2024

Crossrefs

Cf. A000295, A091090, A376116, A376131.

Sequence in context: A050338 A301598 A077088 * A348971 A358821 A297420

Adjacent sequences: A376129 A376130 A376131 * A376133 A376134 A376135

Keyword

nonn

Author

Ryota Inagaki, Tanya Khovanova, and Austin Luo, Sep 11 2024

Status

approved