|
|
A349840
|
|
The number of compositions of n using elements from the set {1,3,5,7,8}.
|
|
2
|
|
|
1, 1, 1, 2, 3, 5, 8, 13, 22, 35, 56, 91, 147, 238, 385, 623, 1009, 1632, 2640, 4272, 6912, 11184, 18096, 29280, 47377, 76657, 124033, 200690, 324723, 525413, 850136, 1375549, 2225686, 3601235, 5826920, 9428155
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Number of ways to tile an n-board (an n X 1 array of 1 X 1 cells) using squares, trominoes, pentominoes, heptominoes, and octominoes.
Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-1,0,2,4,6,7} for all i=1,...,n.
a(n) gives the sums of the antidiagonals of A349839.
|
|
REFERENCES
|
D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), North-Holland, Amsterdam, 1970, pp. 755-770.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-7) + a(n-8) + delta(n,0), a(n<0)=0 (where delta(i,j) is the Kronecker delta).
a(n) = a(n-1) + a(n-2) + a(n-8) - a(n-9) - a(n-10) + delta(n,0) - delta(n,2), a(n<0)=0.
G.f.: 1/(1-x-x^3-x^5-x^7-x^8).
|
|
MATHEMATICA
|
CoefficientList[Series[1/(1-x-x^3-x^5-x^7-x^8), {x, 0, 35}], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|