OFFSET
1,1
COMMENTS
Conjecture: a(n) is the disorder number of the Aztec diamond of size n.
REFERENCES
G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge University Press, 2004.
LINKS
Sela Fried, The disorder number of a graph, arXiv:2208.03788 [math.CO], 2022.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: x*(5 + 17*x - 9*x^2 + 3*x^3)/(1 - x)^4. - Stefano Spezia, Oct 26 2022
MATHEMATICA
Table[(8n^3+12n^2+4n-9)/3, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {5, 37, 109, 237}, 40] (* Harvey P. Dale, Nov 20 2022 *)
PROG
(Python)
def A358035(n): return n*(n*((n<<3) + 12) + 4)//3 - 3 # Chai Wah Wu, Oct 31 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sela Fried, Oct 26 2022
STATUS
approved