A243646 - OEIS

A243646

Number of ways three L-tiles can be placed on an n X n square.

0, 0, 0, 0, 11, 196, 1195, 4544, 13215, 32276, 69671, 137120, 251139, 434180, 715891, 1134496, 1738295, 2587284, 3754895, 5329856, 7418171, 10145220, 13657979, 18127360, 23750671, 30754196, 39395895, 49968224, 62801075, 78264836, 96773571, 118788320, 144820519

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

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

FORMULA

G.f.: x^4*(x^5-27*x^4+90*x^3-54*x^2-119*x-11) / (x-1)^7.

a(n) = (n^6-6*n^5-6*n^4+88*n^3-73*n^2-310*n+426)/6 for n>=4, a(n) = 0 for n<4.

EXAMPLE

a(4) = 11:

._______. ._______. ._______. ._______.

| |_|_|_| | |_|_|_| | |_| |_| | |_| |_|

|___|_|_| |___| |_| |___|___| |___|___|

| |_| |_| | |_|___| | |_|_|_| |_| |_|_|

|___|___| |___|_|_| |___|_|_| |_|___|_|

._______. ._______. ._______. ._______.

| |_| |_| |_|_| |_| |_|_| |_| |_| |_|_|

|___|___| | |_|___| |_|_|___| |_|___|_|

|_|_| |_| |___| |_| | |_| |_| | |_| |_|

|_|_|___| |_|_|___| |___|___| |___|___|

._______. ._______. ._______.

|_|_| |_| | |_|_|_| |_| |_|_|

|_| |___| |___| |_| | |___|_|

| |___|_| |_| |___| |___| |_|

|___|_|_| |_|___|_| |_|_|___| .

MAPLE

a:= n-> `if`(n<4, 0, ((((((n-6)*n-6)*n+88)*n-73)*n-310)*n+426)/6):

seq(a(n), n=0..50);

CROSSREFS

Column k=3 of A243608.

Sequence in context: A201185 A345342 A218818 * A186251 A234628 A105124

Adjacent sequences: A243643 A243644 A243645 * A243647 A243648 A243649

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jun 08 2014

STATUS

approved