login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A187753 Number of different ways to divide an n X 5 rectangle into subsquares, considering only the list of parts. 2
1, 1, 3, 5, 9, 11, 20, 26, 36, 48, 64, 80, 106, 128, 160, 195, 238, 281, 340, 397, 467, 544, 633, 724, 838, 950, 1083, 1226, 1385, 1550, 1745, 1942, 2165, 2402, 2663, 2933, 3242, 3555, 3902, 4270, 4667, 5079, 5539, 6007, 6518, 7055, 7631, 8227, 8880, 9547 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

G.f.: (x^9 - x^8 + x^7 - 4*x^6 + x^5 - 3*x^4 - x^3 - 2*x^2 - 1) / (x^19 - x^18 - x^16 + 2*x^12 + x^10 - x^9 - 2*x^7 + x^3 + x - 1).

EXAMPLE

a(4) = 9 because there are 9 ways to divide a 4 X 5 rectangle into subsquares, considering only the list of parts: [20(1 X 1)], [16(1 X 1), 1(2 X 2)], [12(1 X 1), 2(2 X 2)], [11(1 X 1), 1(3 X 3)], [8(1 X 1), 3(2 X 2)], [7(1 X 1), 1(2 X 2), 1(3 X 3)], [4(1 X 1), 4(2 X 2)], [4(1 X 1), 1(4 X 4)], [3(1 X 1), 2(2 X 2), 1(3 X 3)].  There is no way to divide this rectangle into [2(1 X 1), 2(3 X 3)].

MAPLE

gf:= (x^9-x^8+x^7-4*x^6+x^5-3*x^4-x^3-2*x^2-1)/

     (x^19-x^18-x^16+2*x^12+x^10-x^9-2*x^7+x^3+x-1):

a:= n-> coeff(series(gf, x, n+1), x, n):

seq(a(n), n=0..60);

PROG

(MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x^2+x^3+3*x^4-x^5+4*x^6-x^7+x^8-x^9)/((1-x)^5*(1+x)^2*(1+x^2)*(1-x +x^2)*(1+x+x^2)^2*(1+x+x^2+x^3+x^4)))); // Bruno Berselli, Apr 17 2013

CROSSREFS

Column k=5 of A224697.

Sequence in context: A034760 A070639 A078392 * A231716 A113488 A092917

Adjacent sequences:  A187750 A187751 A187752 * A187754 A187755 A187756

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Apr 17 2013

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 April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)