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A212676 Number of (w,x,y,z) with all terms in {1,...,n} and w+x=|x-y|+|y-z|. 2
0, 0, 1, 9, 23, 52, 92, 155, 234, 344, 475, 645, 841, 1084, 1358, 1687, 2052, 2480, 2949, 3489, 4075, 4740, 5456, 6259, 7118, 8072, 9087, 10205, 11389, 12684, 14050, 15535, 17096, 18784, 20553, 22457, 24447, 26580, 28804, 31179, 33650 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
For a guide to related sequences, see A211795.
LINKS
FORMULA
a(n)=2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
G.f.: (x^2 + 7*x^3 + 4*x^4 + x^5)/(1 - 2 x - x^2 + 4 x^3 - x^4 - 2 x^5 + x^6)
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x == Abs[x - y] + Abs[y - z], s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212676 *)
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 0, 1, 9, 23, 52}, 41]
CROSSREFS
Cf. A211795.
Sequence in context: A159221 A079040 A183338 * A211478 A147420 A259170
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 23 2012
STATUS
approved

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Last modified June 13 23:50 EDT 2024. Contains 373391 sequences. (Running on oeis4.)