A027558 - OEIS

A027558

Number of 3-unbalanced strings of length n (= 2^n - A027557(n)).

0, 0, 0, 0, 2, 6, 20, 50, 126, 288, 654, 1422, 3068, 6474, 13574, 28112, 57942, 118566, 241788, 490914, 994334, 2008512, 4050398, 8154014, 16396668, 32935194, 66104982, 132586416, 265792070, 532579830, 1066790972

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OFFSET

0,5

COMMENTS

a(n) is also the number of different ways to fold down a folding yardstick with n sticks (stick length is one) to form an equilateral tetragon (parallelogram) with side length one. - Frank Hollstein, May 01 2019

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (3,1,-8,2,4).

FORMULA

a(n) = 2*A005674(n).

G.f.: -2*x^4/((2*x-1)*(2*x^2-1)*(x^2+x-1)). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]

PROG

(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; 4, 2, -8, 1, 3]^n*[0; 0; 0; 0; 2])[1, 1] \\ Charles R Greathouse IV, Jun 02 2026

CROSSREFS

Cf. A027557, A005674.

Sequence in context: A121128 A056820 A204422 * A320910 A066397 A060344

Adjacent sequences: A027555 A027556 A027557 * A027559 A027560 A027561

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, David Callan

STATUS

approved