|
|
A202077
|
|
Number of arrays of 5 integers in -n..n with sum zero and the sum of every adjacent pair being odd.
|
|
1
|
|
|
2, 26, 78, 264, 504, 1128, 1786, 3262, 4660, 7540, 10092, 15066, 19278, 27174, 33644, 45428, 54846, 71622, 84770, 107780, 125532, 156156, 179478, 219234, 249184, 299728, 337456, 400582, 447330, 524970, 582072, 676296, 745178, 858194, 940374
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9).
G.f.: 2*x*(1 + 12*x + 22*x^2 + 45*x^3 + 22*x^4 + 12*x^5 + x^6) / ((1 - x)^5*(1 + x)^4).
a(n) = (230*n^4 + 552*n^3 + 424*n^2 + 96*n) / 384 for n even.
a(n) = (230*n^4 + 368*n^3 + 148*n^2 + 16*n + 6) / 384 for n odd.
(End)
|
|
EXAMPLE
|
Some solutions for n=3:
-2 0 0 -2 0 2 0 0 2 2 -2 2 2 2 -2 2
-1 -1 -3 1 -1 -1 -1 3 1 -3 3 1 -3 -3 1 -3
0 2 2 0 0 0 2 -2 -2 -2 2 0 0 2 -2 0
1 -3 1 -1 -1 -1 1 -1 -1 3 -3 -3 -1 -1 3 3
2 2 0 2 2 0 -2 0 0 0 0 0 2 0 0 -2
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|