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A212506 Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y<=2z. 2
0, 1, 16, 64, 196, 441, 900, 1600, 2704, 4225, 6400, 9216, 12996, 17689, 23716, 30976, 40000, 50625, 63504, 78400, 96100, 116281, 139876, 166464, 197136, 231361, 270400, 313600, 362404, 416025, 476100, 541696, 614656, 693889, 781456 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211795.
LINKS
FORMULA
a(n) = 2a(n-1)+2a(n-2)-6a(n-3)+6a(n-5)-2a(n-6)-2a(n-7)+a(n-8).
From Alois P. Heinz, May 31 2012: (Start)
a(n) = A006578(n)^2.
G.f.: x*(14*x+30*x^2+42*x^3+17*x^4+4*x^5+1) / ((x+1)^3*(1-x)^5). (End)
MAPLE
a:= n-> (n*(n+1)/2+floor(n^2/4))^2:
seq(a(n), n=0..60); # Alois P. Heinz, May 31 2012
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w <= 2 x && y <= 2 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212506 *)
CROSSREFS
Cf. A211795.
Sequence in context: A316542 A306057 A059165 * A212512 A317235 A255661
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 19 2012
STATUS
approved

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Last modified July 25 15:15 EDT 2024. Contains 374611 sequences. (Running on oeis4.)