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A247268 Number of tilings of a 5 X n rectangle using n pentominoes of shapes Y, U, X. 6
1, 0, 0, 1, 0, 2, 1, 0, 4, 5, 38, 22, 13, 90, 144, 457, 408, 386, 1267, 2230, 5912, 6481, 7098, 18896, 35433, 79634, 101232, 127501, 288304, 546652, 1113907, 1560356, 2148298, 4408181, 8335234, 15954116, 23827541, 35011426, 67591204, 126376945, 232719926 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

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

Wikipedia, Pentomino

FORMULA

G.f.: see Maple program.

EXAMPLE

a(3) = 1, a(5) = 2:

._____.     ._________.   ._________.

| ._. |     |_. .___| |   | |___. ._|

|_| |_|     | |_| |_. |   | ._| |_| |

|_. ._|  ,  | |_. ._| |   | |_. ._| |

| |_| |     | ._|_| |_|   |_| |_|_. |

|_____|     |_|_______|   |_______|_|  .

MAPLE

gf:= -(x^40 +12*x^39 +36*x^38 -5*x^36 -2*x^35 +12*x^34 +54*x^33 +4*x^32 -21*x^31 -23*x^30 +4*x^29 +20*x^28 +4*x^27 -4*x^25 -7*x^24 -6*x^23 -3*x^22 +33*x^21 -7*x^20 -10*x^19 -12*x^18 -9*x^17 +12*x^16 +16*x^15 +3*x^14 -2*x^13 -2*x^12 -2*x^11 -3*x^10 +5*x^9 -2*x^6 -7*x^5 -x^4 +1) /

(x^43 +12*x^42 +36*x^41 -3*x^40 -29*x^39 -58*x^38 +12*x^37 +67*x^36 +4*x^35 -123*x^34 -99*x^33 +8*x^32 +23*x^31 -145*x^30 -52*x^29 -52*x^28 -35*x^27 -112*x^26 -99*x^25 -28*x^24 -7*x^23 -15*x^22 -99*x^21 -42*x^20 +22*x^19 +36*x^18 +26*x^17 -4*x^16 +6*x^15 +31*x^14 +5*x^13 +11*x^12 +14*x^11 +23*x^10 -5*x^9 -7*x^8 -x^7 +2*x^6 +9*x^5 +x^4 +x^3 -1):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..60);

CROSSREFS

Cf. A174249, A233427, A247124, A247125.

Sequence in context: A073592 A164994 A269952 * A266867 A151852 A300864

Adjacent sequences:  A247265 A247266 A247267 * A247269 A247270 A247271

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 30 2014

STATUS

approved

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Last modified June 6 11:14 EDT 2020. Contains 334827 sequences. (Running on oeis4.)