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A358035
a(n) = (8*n^3 + 12*n^2 + 4*n - 9)/3.
1
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
1,1
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.
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
Cf. A354528.
Sequence in context: A142036 A089195 A249861 * A319485 A201119 A263783
KEYWORD
nonn,easy
AUTHOR
Sela Fried, Oct 26 2022
STATUS
approved