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A212767
Number of (w,x,y,z) with all terms in {0,...,n}, w even, x even, and w+x=y+z.
2
1, 1, 8, 10, 29, 35, 72, 84, 145, 165, 256, 286, 413, 455, 624, 680, 897, 969, 1240, 1330, 1661, 1771, 2168, 2300, 2769, 2925, 3472, 3654, 4285, 4495, 5216, 5456, 6273, 6545, 7464, 7770, 8797, 9139, 10280, 10660, 11921, 12341, 13728, 14190
OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211795.
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+4*x^2+2*x^3+x^4 ) / ( (1+x)^3*(1-x)^4 ).
a(n) = (4*n^3+15*n^2+20*n+12+3*(n^2+4*n+4)*(-1)^n)/24. - Luce ETIENNE, Jun 03 2014
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 0 && w + x == y + z), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 50]] (* A212767 *)
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 1, 8, 10, 29, 35, 72}, 50]
CROSSREFS
Cf. A211795.
Sequence in context: A024869 A108940 A007939 * A126807 A230110 A223587
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 29 2012
STATUS
approved