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A077909 Expansion of 1/((1-x)*(1+x+x^2+2*x^3)). 5
1, 0, 0, -1, 2, 0, 1, -4, 4, -1, 6, -12, 9, -8, 24, -33, 26, -40, 81, -92, 92, -161, 254, -276, 345, -576, 784, -897, 1266, -1936, 2465, -3060, 4468, -6337, 7990, -10588, 15273, -20664, 26568, -36449, 51210, -67896, 89585, -124108, 170316, -225377, 303278, -418532, 566009, -754032, 1025088 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The absolute value of a(n) is the number of tilings of a 5 X n rectangle using n pentominoes of shapes N, U, X. |a(3)| = 1, |a(4)| = 2:

._____.     ._______.  ._______.

| ._. |     | ._. | |  | | ._. |

|_| |_|     |_| |_| |  | |_| |_|

|_. ._|  ,  | ._| ._|  |_. |_. |

| |_| |     | | |_| |  | |_| | |

|_____|     |_|_____|  |_____|_|. - Alois P. Heinz, Jan 03 2014

LINKS

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

Wikipedia, Pentomino

Index entries for linear recurrences with constant coefficients, signature (0,0,-1,2)

FORMULA

a(n) = (-1)^n*sum(A128099(n-2*k, n-3*k), k=0..floor(n/3)). - Johannes W. Meijer, Aug 28 2013

G.f.: 1/(1 + x^3 - 2*x^4). - Arkadiusz Wesolowski, Nov 20 2013

MAPLE

a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <2|-1|0|0>>^n.

        <<1, 0, 0, -1>>)[1, 1]:

seq(a(n), n=0..60);  # Alois P. Heinz, Nov 20 2013

MATHEMATICA

CoefficientList[1/(1+x^3-2*x^4) + O[x]^60, x] (* Jean-Fran├žois Alcover, Jun 08 2015, after Arkadiusz Wesolowski *)

PROG

(PARI) Vec( 1/((1-x)*(1+x+x^2+2*x^3)) +O(x^66)) \\ Joerg Arndt, Aug 28 2013

CROSSREFS

Partial sums of A077976.

Cf. A174249, A233427, A234312, A234931, A247126.

Sequence in context: A158984 A158417 A139435 * A247126 A342134 A327117

Adjacent sequences:  A077906 A077907 A077908 * A077910 A077911 A077912

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified June 20 21:27 EDT 2021. Contains 345255 sequences. (Running on oeis4.)