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A220128 1 followed by period 6: (1, 3, 2, 3, 1, 4) repeated; offset 0. 2
1, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of tilings of an n X 3 rectangle using integer-sided rectangular tiles of area n.

Also decimal expansion of 12443/109890 = 0.1132314132314... .

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1).

FORMULA

G.f.: (-3*x^4-4*x^3-4*x^2-2*x-1) / (x^4+x^3-x-1).

From Wesley Ivan Hurt, Jun 20 2016: (Start)

a(n) + a(n-1) = a(n-3) + a(n-4) for n>4.

a(0) = 1, a(n) = (7 + 3*cos(n*Pi) + 2*cos(2*n*Pi/3))/3 for n>0. (End)

E.g.f.: 2*(-9/2 + cos(sqrt(3)*x/2)*exp(-x/2) + 2*sinh(x) + 5*cosh(x))/3. - Ilya Gutkovskiy, Jun 21 2016

EXAMPLE

a(6) = 4, because there are 4 tilings of a 6 X 3 rectangle using integer-sided rectangular tiles of area 6:

._._._.  .___._.  ._.___.  ._____.

| | | |  |   | |  | |   |  |     |

| | | |  |   | |  | |   |  |_____|

| | | |  |___| |  | |___|  |     |

| | | |  |   | |  | |   |  |_____|

| | | |  |   | |  | |   |  |     |

|_|_|_|  |___|_|  |_|___|  |_____|

MAPLE

a:=n-> `if`(n=0, 1, [4, 1, 3, 2, 3, 1][irem(n, 6)+1]): seq(a(n), n=0..100);

MATHEMATICA

PadRight[{1}, 120, {4, 1, 3, 2, 3, 1}] (* Harvey P. Dale, Jan 06 2016 *)

PROG

(MAGMA) [1] cat &cat [[1, 3, 2, 3, 1, 4]^^20]; // Wesley Ivan Hurt, Jun 20 2016

CROSSREFS

Row n=3 of A220122.

Sequence in context: A106584 A213940 A236027 * A324468 A131498 A236455

Adjacent sequences:  A220125 A220126 A220127 * A220129 A220130 A220131

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Dec 06 2012

STATUS

approved

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Last modified September 27 15:44 EDT 2021. Contains 347691 sequences. (Running on oeis4.)