A370109 a(n) = n^2*(2*n^2-23).

-21, -60, -45, 144, 675, 1764, 3675, 6720, 11259, 17700, 26499, 38160, 53235, 72324, 96075, 125184, 160395, 202500, 252339, 310800, 378819, 457380, 547515, 650304, 766875, 898404, 1046115, 1211280, 1395219, 1599300, 1824939, 2073600, 2346795, 2646084, 2973075

Offset

1,1

Comments

For n > 5, also the number of chordless cycles (all of length 4) in the torus grid graph C_n square C_n.

Links

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Chordless Cycle

Eric Weisstein's World of Mathematics, Graph Complement

Eric Weisstein's World of Mathematics, Torus Grid Graph

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

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: 3*(7-15*x-15*x^2+7*x^3)/(-1+x)^5.

Mathematica

Table[n^2 (2 n^2 - 23), {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {-21, -60, -45, 144, 675}, 20]
CoefficientList[Series[3 (7 - 15 x - 15 x^2 + 7 x^3)/(-1 + x)^5, {x, 0, 20}], x]

Crossrefs

Sequence in context: A370519 A037305 A379182 * A223467 A051873 A223460

Adjacent sequences: A370106 A370107 A370108 * A370110 A370111 A370112

Keyword

sign,easy

Author

Eric W. Weisstein, Feb 10 2024

Status

approved