login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A254125 The number of tilings of a 4 X n rectangle using integer length rectangles with at least one side of length 1, i.e., tiles are 1 X 1, 1 X 2, ..., 1 X n, 2 X 1, 3 X 1, 4 X 1. 7
1, 8, 124, 2408, 50128, 1064576, 22734496, 486248000, 10404289216, 222647030144, 4764694602112, 101966374503680, 2182126445631232, 46698521255409152, 999370260391863808, 21386993399983588352, 457691719382960757760, 9794818132582234683392 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let G_n be the graph with vertices {(a,b) : 1<=a<=7, 1<=b<=2n-1, a+b odd} and edges between (a,b) and (c,d) if and only if |a-b|=|c-d|=1.  Then a(n) is the number of independent sets in G_n.

LINKS

Table of n, a(n) for n=0..17.

Z. Zhang, Merrifield-Simmons index of generalized Aztec diamond and related graphs, MATCH Commun. Math. Comput. Chem. 56 (2006) 625-636.

FORMULA

G.f.: (1 - 22x + 86x^2 - 92x^3 + 16x^4)/(1 - 30x + 202x^2 - 396x^3 + 248x^4 - 32x^5).

PROG

(PARI) Vec((1-22*x+86*x^2-92*x^3+16*x^4)/(1-30*x+202*x^2-396*x^3 +248*x^4-32*x^5) + O(x^30)) \\ Michel Marcus, Jan 26 2015

CROSSREFS

Cf. A052961, A254124, A254126, A254127.

Column k=4 of A254414.

Sequence in context: A120957 A302356 A069459 * A024282 A231638 A065082

Adjacent sequences:  A254122 A254123 A254124 * A254126 A254127 A254128

KEYWORD

nonn,easy

AUTHOR

Steve Butler, Jan 25 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 12:28 EST 2019. Contains 329862 sequences. (Running on oeis4.)