|
|
A212760
|
|
Number of (w,x,y,z) with all terms in {0,...,n}, w even, and x = y + z.
|
|
5
|
|
|
1, 3, 12, 20, 45, 63, 112, 144, 225, 275, 396, 468, 637, 735, 960, 1088, 1377, 1539, 1900, 2100, 2541, 2783, 3312, 3600, 4225, 4563, 5292, 5684, 6525, 6975, 7936, 8448, 9537, 10115, 11340, 11988, 13357, 14079, 15600, 16400, 18081, 18963, 20812, 21780, 23805
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
For a guide to related sequences, see A211795.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7).
G.f.: ( 1+2*x+6*x^2+2*x^3+x^4 ) / ( (1+x)^3*(1-x)^4 ).
|
|
MAPLE
|
|
|
MATHEMATICA
|
t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && x == y + z, s++],
{w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 50]] (* A212760 *)
Table[(n + 1) (n + 2) (2 n + 3 + (-1)^n)/8, {n, 0, 50}] (* Wesley Ivan Hurt, Jul 22 2014 *)
CoefficientList[Series[(1 + 2 x + 6 x^2 + 2 x^3 + x^4)/((1 + x)^3 (1 - x)^4), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 23 2014 *)
|
|
PROG
|
(Magma) [(n+1)*(n+2)*(2*n+3+(-1)^n)/8 : n in [0..50]]; // Wesley Ivan Hurt, Jul 22 2014
(Haskell)
a212760 = a260706 . fromInteger . a001318 . (+ 1)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|