A348154 - OEIS

A348154

Number of inequivalent strip arrangements.

1, 3, 11, 100, 1063, 15686, 271975, 5509456, 126604661, 3256687324, 92655915831, 2888838414540, 97940953019995, 3587315304010374, 141162897496953263, 5939167862427259456, 266046178356979847881, 12641661811772879875640, 635092155152649300232063, 33633813271235206436451100

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OFFSET

1,2

COMMENTS

Given n strips, each of length n squares (dimensions 1 X n), a(n) is the number of distinct shapes that can be created by setting the strips side by side while satisfying the condition that the shape must include at least one row of length L=n squares (row considered to be a direction measured perpendicular to the strips). Shapes differing only by a rotation are considered to be equivalent.

LINKS

Table of n, a(n) for n=1..20.

Joseph Rozhenko, Illustration of a(3) = 11

FORMULA

From Jinyuan Wang, Oct 08 2021: (Start)

a(2*k+1) = ((2*k+1)^(2*k+1) - (2*k)^(2*k+1) + (2*k+1)^k) / 2.

a(2*k) = ((2*k)^(2*k) - (2*k-1)^(2*k) + (2*k)^k + (2*k-1)^k) / 2.

(End)

PROG

(PARI) a(n) = (n^n - (n-1)^n + n^(n\2) + !(n%2)*(n-1)^(n\2))/2; \\ Jinyuan Wang, Oct 08 2021

CROSSREFS

Cf. A045531 (when rotations are considered distinct).