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

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).

Sequence in context: A123996 A201425 A008561 * A072640 A154299 A007616

Adjacent sequences: A348151 A348152 A348153 * A348155 A348156 A348157

Keyword

nonn

Author

Joseph Rozhenko, Oct 04 2021

Extensions

More terms from Jinyuan Wang, Oct 08 2021

Status

approved