A370649 Dimension of space of equivariant linear maps from R^{n^3} to R^{n^3} under diagonal action of {-1, 1}^n.

0, 1, 32, 183, 544, 1205, 2256, 3787, 5888, 8649, 12160, 16511, 21792, 28093, 35504, 44115, 54016, 65297, 78048, 92359, 108320, 126021, 145552, 167003, 190464, 216025, 243776, 273807, 306208, 341069, 378480, 418531, 461312, 506913, 555424, 606935, 661536, 719317

Offset

0,3

Links

Table of n, a(n) for n=0..37.

D. Lim, J. Robinson, S. Jegelka, and H. Maron, Expressive Sign Equivariant Networks for Spectral Geometric Learning, Conference on Neural Information Processing Systems (NeurIPS), 2023. See Table 4 at p. 24.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (1/2^n) * Sum_{s in {-1,1}^n} (s_1 + s_2 + ... + s_n)^6 [from Proposition 7 of Lim et al.]. - Sean A. Irvine, Jul 14 2024

From Alois P. Heinz, Jul 14 2024: (Start)

a(n) = 2^(-n) * Sum_{k=0..n} (2*k-n)^6 * binomial(n,k).

G.f.: x*(61*x^2+28*x+1)/(x-1)^4.

a(n) = 15*n^3 - 30*n^2 + 16*n. (End)

E.g.f.: exp(x)*x*(1 + 15*x + 15*x^2). - Stefano Spezia, Jul 15 2024

Maple

a:= n-> ((15*n-30)*n+16)*n:
seq(a(n), n=0..37);  # Alois P. Heinz, Jul 14 2024

Prog

(Python)
def A370649(n): return n*(15*(n-1)**2+1) # Chai Wah Wu, Jul 15 2024

Crossrefs

Cf. A000567.

Sequence in context: A231299 A029534 A120046 * A303798 A305243 A304477

Adjacent sequences: A370646 A370647 A370648 * A370650 A370651 A370652

Keyword

nonn,easy,new

Author

Derek Lim, Feb 25 2024

Extensions

a(21)-a(33) from Sean A. Irvine, Jul 14 2024

a(34)-a(37) from Alois P. Heinz, Jul 14 2024

Status

approved