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A247710 Number T(n,k) of tilings of a 5 X n rectangle with pentominoes of any shape and exactly k pentominoes of shape W; triangle T(n,k), n>=0, 0<=k<=max(0,floor((n-2)/2)*2) read by rows. 5
1, 1, 5, 56, 461, 32, 8, 3558, 368, 80, 23966, 3256, 696, 24, 8, 178127, 29564, 6558, 360, 80, 1362597, 266672, 61858, 4852, 770, 24, 8, 10194184, 2361632, 581452, 58732, 8890, 384, 80, 75684682, 20056764, 5220634, 632044, 97174, 5968, 914, 24, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Sum_{k>0} k * T(n,k) = A247743(n).
LINKS
Wikipedia, Pentomino
EXAMPLE
T(4,2) = 8:
._______. ._______. ._______.
| ._____| |_. |_. | | ._____|
|_| ._| | | |_. | | |_| ._| |
| ._| ._| | | |_| | | ._| | |
|_|___| | | |_. |_| |_| ._| |
|_______| (*2) |___|___| (*2) |___|___| (*4)
Triangle T(n,k) begins:
00 : 1;
01 : 1;
02 : 5;
03 : 56;
04 : 461, 32, 8;
05 : 3558, 368, 80;
06 : 23966, 3256, 696, 24, 8;
07 : 178127, 29564, 6558, 360, 80;
08 : 1362597, 266672, 61858, 4852, 770, 24, 8;
09 : 10194184, 2361632, 581452, 58732, 8890, 384, 80;
10 : 75684682, 20056764, 5220634, 632044, 97174, 5968, 914, 24, 8;
CROSSREFS
Row sums give A174249 or A233427(n,5).
Column k=0 gives A247774.
Cf. A247743.
Sequence in context: A288543 A062125 A030060 * A247774 A258490 A255953
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 23 2014
STATUS
approved

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Last modified February 21 14:42 EST 2024. Contains 370236 sequences. (Running on oeis4.)