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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A062200 Number of compositions of n such that two adjacent parts are not equal modulo 2. 8
1, 1, 1, 3, 2, 6, 6, 11, 16, 22, 37, 49, 80, 113, 172, 257, 377, 573, 839, 1266, 1874, 2798, 4175, 6204, 9274, 13785, 20577, 30640, 45665, 68072, 101393, 151169, 225193, 335659, 500162, 745342, 1110790, 1655187, 2466760, 3675822, 5477917, 8163217, 12164896, 18128529, 27015092 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also (0,1)-strings such that all maximal blocks of 1's have even length and all maximal blocks of 0's have odd length.

REFERENCES

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(Problems 2.4.3, 2.4.13).

LINKS

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (0, 2, 1, -1).

FORMULA

a(n) = Sum_{j=0..n+1} binomial(n-j+1, 3*j-n+1).

a(n) = 2*a(n-2) + a(n-3) - a(n-4).

G.f.: -(x^2-x-1)/(x^4-x^3-2*x^2+1). More generally, g.f. for the number of compositions of n such that two adjacent parts are not equal modulo p is 1/(1-Sum_{i=1..p} x^i/(1+x^i-x^p)).

G.f.: W(0)/(2*x^2) -1/x^2, where W(k) = 1 + 1/(1 - x*(k - x)/( x*(k+1 - x) - 1/W(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Aug 28 2013

EXAMPLE

From Joerg Arndt, Oct 27 2012:  (Start)

The 11 such compositions of n=7 are

[ 1]  1 2 1 2 1

[ 2]  1 6

[ 3]  2 1 4

[ 4]  2 3 2

[ 5]  2 5

[ 6]  3 4

[ 7]  4 1 2

[ 8]  4 3

[ 9]  5 2

[10]  6 1

[11]  7

The 16 such compositions of n=8 are

[ 1]  1 2 1 4

[ 2]  1 2 3 2

[ 3]  1 2 5

[ 4]  1 4 1 2

[ 5]  1 4 3

[ 6]  1 6 1

[ 7]  2 1 2 1 2

[ 8]  2 1 2 3

[ 9]  2 1 4 1

[10]  2 3 2 1

[11]  3 2 1 2

[12]  3 2 3

[13]  3 4 1

[14]  4 1 2 1

[15]  5 2 1

[16]  8

(End)

MATHEMATICA

LinearRecurrence[{0, 2, 1, -1}, {1, 1, 1, 3}, 50] (* Harvey P. Dale, Feb 26 2012 *)

Join[{1}, Table[Sum[ Binomial[n-j+1, 3j-n+1], {j, 0, n-1}], {n, 50}]] (* Harvey P. Dale, Feb 26 2012 *)

PROG

(PARI) x='x+O('x^66); Vec(-(x^2-x-1)/(x^4-x^3-2*x^2+1)) \\ Joerg Arndt, May 13 2013

CROSSREFS

Cf. A003242, A062201-A062203.

Sequence in context: A154028 A157793 A096375 * A114208 A014686 A053090

Adjacent sequences:  A062197 A062198 A062199 * A062201 A062202 A062203

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jun 13 2001

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 17:56 EST 2017. Contains 294894 sequences.