A155901 Number of sizes k such that the 2-adic valuation of the number of k X k alternating sign matrices is n.

2, 8, 5, 12, 5, 14, 8, 14, 6, 24, 9, 16, 8, 12, 10, 22, 8, 22, 8, 22, 7, 28

Offset

1,1

Comments

These are the values from Table 1 on p. 14 of Sun and Moll.

References

D. Bressoud, Proofs and Confirmations: the story of the Alternating Sign Matrix Conjecture, Cambridge University Press, 1999.

Links

Table of n, a(n) for n=1..22.

D. Bressoud and J. Propp, How the Alternating Sign Matrix Conjecture was solved, Notices Amer. Math. Soc., 46:637-646, 1999.

Xinyu Sun and Victor H. Moll, The p-adic valuations of sequences counting alternating sign matrices, arXiv:0901.4564 [math.NT], 2009.

Andrei Zabolotskii, Rust program.

Formula

a(n) = #{k: A194827(k) = n}.

Example

a(7) = 8 because "the eight solutions to Nu(T(n)) = 7 are 26, 38, 46, 82, 5462, 10922, 10924 and J_15 - 1 = 21844" where J_k = k-th Jacobsthal number = A001045(k+1).

Prog

(SageMath)
def s(n): return int(n).bit_count()
def upto(n):
    a, x = [0] * n, 0
    for i in (1..lucas_number1(2*n+2, 1, -2)):
        x += s(2*i-2) + s(2*i-1) - s(i-1) - s(3*i-2)
        if x and x <= n: a[x-1] += 1
    return a # Andrei Zabolotskii, Oct 27 2025

Crossrefs

Cf. A000219, A001045, A005130, A048601, A128445, A143670, A194827.

Sequence in context: A185583 A309792 A318725 * A029745 A332067 A183232

Adjacent sequences: A155898 A155899 A155900 * A155902 A155903 A155904

Keyword

nonn,more

Author

Jonathan Vos Post, Jan 30 2009

Extensions

Edited and extended with a(9)-a(22) by Andrei Zabolotskii, Oct 29 2025

Status

approved