A358035 a(n) = (8*n^3 + 12*n^2 + 4*n - 9)/3.

5, 37, 109, 237, 437, 725, 1117, 1629, 2277, 3077, 4045, 5197, 6549, 8117, 9917, 11965, 14277, 16869, 19757, 22957, 26485, 30357, 34589, 39197, 44197, 49605, 55437, 61709, 68437, 75637, 83325, 91517, 100229, 109477, 119277, 129645, 140597, 152149, 164317

Offset: 1

Author

Sela Fried, Oct 26 2022

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A354528.

Programs

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 *)

Python

def A358035(n): return n*(n*((n<<3) + 12) + 4)//3 - 3 # Chai Wah Wu, Oct 31 2022

Formula

G.f.: x*(5 + 17*x - 9*x^2 + 3*x^3)/(1 - x)^4. - Stefano Spezia, Oct 26 2022