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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A228577 The number of 1-length gaps in all possible covers of n-length line by 2-length segments. 3
0, 1, 0, 2, 2, 3, 6, 7, 12, 17, 24, 36, 50, 72, 102, 143, 202, 282, 394, 549, 762, 1057, 1462, 2019, 2784, 3832, 5268, 7232, 9916, 13581, 18580, 25394, 34674, 47303, 64478, 87819, 119520, 162549, 220920, 300060, 407302, 552552, 749186, 1015259, 1375134 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

2-gaps must be filled, so, for example, xxoo doesn't count for n=4. - Jon Perry, Nov 18 2014

LINKS

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

D. Birmajer, J. Gil and M. Weiner, Linear recurrence sequences and their convolutions via Bell polynomials, arXiv:1405.7727 [math.CO], 2014  and J. Int. Seq. 18 (2015) # 15.1.2.

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

FORMULA

For n>1, a(n) = n * A228361(n) - 2 * A228364(n).

G.f.: x/(x^3 + x^2 - 1)^2, convolution of A182097 by itself.

a(n) = 2*a(n-2) +2*a(n-3) -a(n-4) -2*a(n-5) -a(n-6) for n>5.

(n-1)*a(n) - (n+1)*a(n-2) - (n+2)*a(n-3) = 0 for n>2. - Michael D. Weiner, Nov 18 2014

EXAMPLE

For n=6 we have xxoxxo, oxxxxo and oxxoxx, so a(6) = number of o's = 6. - Jon Perry, Nov 18 2014

MAPLE

A228577 := proc(n) coeftayl(x/(x^3+x^2-1)^2, x=0, n); end proc: seq(A228577(n), n=0..50); # Wesley Ivan Hurt, Nov 17 2014

MATHEMATICA

CoefficientList[Series[x/(x^3 + x^2 - 1)^2, {x, 0, 100}], x]

PROG

(MAGMA) I:=[0, 1, 0, 2, 2, 3]; [n le 6 select I[n] else 2*Self(n-2)+2*Self(n-3)-Self(n-4)-2*Self(n-5)-Self(n-6): n in [1..50]]; // Vincenzo Librandi, Nov 18 2014

CROSSREFS

Cf. A228361, A228364.

Sequence in context: A039866 A106369 A298436 * A032062 A303028 A011141

Adjacent sequences:  A228574 A228575 A228576 * A228578 A228579 A228580

KEYWORD

nonn,easy

AUTHOR

Philipp O. Tsvetkov, Aug 26 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 November 17 08:35 EST 2019. Contains 329217 sequences. (Running on oeis4.)