OFFSET
1,3
COMMENTS
Fixed quasi-pentominoes.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(n) = n*(n-1)*(n-2)*(n+1)*(5*n^4-10*n^3-7*n^2+12*n+6)/24.
G.f.: x^3*(114+1884*x+4404*x^2+1884*x^3+114*x^4)/(1-x)^9. [Colin Barker, Apr 25 2012]
EXAMPLE
a(3)=114: there are 114 rotations of the 21 free (possibly) disconnected pentominoes bounded (not necessarily tightly) by an 3*3 square; these include the F, P, T, U, V, W, X and Z (connected) pentominoes and 13 strictly disconnected pentominoes.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Bevan, Jul 27 2009
EXTENSIONS
Example moved to correct section, and ref to free quasi-pentominoes added by David Bevan, Mar 05 2011
STATUS
approved