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A212766
Number of (w,x,y,z) with all terms in {0,...,n}, w even and x odd.
2
0, 4, 18, 64, 150, 324, 588, 1024, 1620, 2500, 3630, 5184, 7098, 9604, 12600, 16384, 20808, 26244, 32490, 40000, 48510, 58564, 69828, 82944, 97500, 114244, 132678, 153664, 176610, 202500, 230640, 262144, 296208, 334084, 374850
OFFSET
0,2
COMMENTS
Every term is even.
For a guide to related sequences, see A211795.
FORMULA
a(n) = 2*a(n-1)+2*a(n-2)-6*a(n-3)+6*a(n-5)-2*a(n-6)-2*a(n-7)+a(n-8).
G.f.: -2*x*(2+5*x+10*x^2+5*x^3+2*x^4) / ( (1+x)^3*(x-1)^5 ).
a(n) = (2n(n+2)-(-1)^n+1)(n+1)^2/8. [Bruno Berselli, Jun 11 2012]
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[(Mod[w, 2] == 0) && (Mod[x, 2] == 1), s++], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];
Map[t[#] &, Range[0, 40]] (* A212766 *)
%/2 (* integers *)
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 4, 18, 64, 150, 324, 588, 1024}, 40]
CROSSREFS
Cf. A211795.
Sequence in context: A227162 A057414 A165910 * A100177 A083321 A362316
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 29 2012
STATUS
approved