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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
OFFSET
0,4
COMMENTS
2-gaps must be filled, so, for example, xxoo doesn't count for n=4. - Jon Perry, Nov 18 2014
REFERENCES
A. G. Shannon, P. G. Anderson and A. F. Horadam, Properties of Cordonnier, Perrin and Van der Laan numbers, International Journal of Mathematical Education in Science and Technology, Volume 37:7 (2006), 825-831. See Eqn. (3.13). - N. J. A. Sloane, Jan 11 2022
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
Sequence in context: A039866 A106369 A298436 * A032062 A303028 A011141
KEYWORD
nonn,easy
AUTHOR
Philipp O. Tsvetkov, Aug 26 2013
STATUS
approved