|
|
A228494
|
|
The number of 3-length segments in all possible covers of L-length line by these segments with allowed gaps < 3.
|
|
0
|
|
|
0, 0, 0, 1, 2, 3, 4, 7, 12, 17, 24, 36, 54, 77, 108, 155, 222, 312, 436, 612, 858, 1194, 1656, 2298, 3184, 4397, 6060, 8346, 11480, 15762, 21612, 29607, 40518, 55385, 75632, 103197, 140692, 191647, 260856, 354814, 482290, 655131, 889364, 1206649, 1636218
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Related with the number of all possible covers of L-length line segment by 3-length line segments with allowed gaps < 3 (A228362).
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0,0,2,2,2,-1,-2,-3,-2,-1)
|
|
FORMULA
|
G.f.: x^3*(x^2+x+1)^2/((x^2+1)*(x^3+x^2-1))^2.
|
|
MATHEMATICA
|
c[k_, l_, m_] := Sum[(-1)^i Binomial[k - 1 - i*l, m - 1] Binomial[m, i], {i, 0, Floor[(k - m)/l]}]; a[L_, l_, m_] := Sum[Binomial[m + 1, m + 1 - j]*c[L - l*m, l - 1, j], {j, 0, m + 1}]; sa[L_, l_] := Sum[j*a[L, l, j], {j, 1, Ceiling[L/l]}]; Table[sa[j, 3], {j, 0, 100}]
CoefficientList[Series[x^3(x^2+x+1)^2/(x^5+x^4+x^3-1)^2, {x, 0, 100}], x]
|
|
PROG
|
(PARI) concat([0, 0, 0], Vec(x^3*(x^2+x+1)^2/((x^2+1)*(x^3+x^2-1))^2+O(x^66))) \\ Joerg Arndt, Aug 23 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|