A374083 Vertical moments of inertia of a unit lozenge tiling of the hexagon with side lengths n (see references for exact configuration).

1, 18, 93, 296, 725, 1506, 2793, 4768, 7641, 11650, 17061, 24168, 33293, 44786, 59025, 76416, 97393, 122418, 151981, 186600, 226821, 273218, 326393, 386976, 455625, 533026, 619893, 716968, 825021, 944850, 1077281, 1223168, 1383393, 1558866, 1750525, 1959336

Offset

1,2

References

J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 6, note a(2) is erroneous in this reference, cf. A071092).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Ilse Fischer, Moments of inertia associated with the lozenge tilings of a hexagon, 2000.

J. Propp, Updated article

J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics

Index entries for sequences related to moment of inertia.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (7*n^4 - n^2) / 6.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) with a(1)=1, a(2)=18, a(3)=93, a(4)=296, a(5)=725. - Vincenzo Librandi, Oct 15 2025

Mathematica

Table[(7*n^4-n^2)/6, {n, 1, 40}] (* Vincenzo Librandi, Oct 15 2025 *)

Prog

(Magma) [(7*n^4 - n^2) / 6 : n in [1..40]]; // Vincenzo Librandi, Oct 15 2025

Crossrefs

Cf. A071092.

Sequence in context: A059138 A117735 A041624 * A227812 A186122 A275253

Adjacent sequences: A374080 A374081 A374082 * A374084 A374085 A374086

Keyword

nonn,easy

Author

Sean A. Irvine, Jun 27 2024

Status

approved