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A212683 Number of (w,x,y,z) with all terms in {1,...,n} and |x-y|=w+|y-z|. 5
0, 0, 2, 8, 22, 46, 84, 138, 212, 308, 430, 580, 762, 978, 1232, 1526, 1864, 2248, 2682, 3168, 3710, 4310, 4972, 5698, 6492, 7356, 8294, 9308, 10402, 11578, 12840, 14190, 15632, 17168, 18802, 20536, 22374, 24318, 26372, 28538, 30820 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)=2*A019298(n-1) for n>=1.

For a guide to related sequences, see A211795.

Also the number of (w,x,y) with all terms in {0,...,n-1} and |w-x|<|x-y|, see A212959. Clark Kimberling, Jun 02 2012

LINKS

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

FORMULA

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).

G.f.: (2*x^2 + 2*x^3 + 2*x^4)/(1 - 3*x + 2*x^2 + 2*x^3 - 3*x^4 + x^5).

a(n)+A212962(n-1) = n^3. _Clark Kimberling, Jun 02 2012

MATHEMATICA

t = Compile[{{n, _Integer}}, Module[{s = 0},

(Do[If[Abs[x - y] == w + Abs[y - z], s = s + 1],

{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

Map[t[#] &, Range[0, 40]]   (* A212683 *)

%/2  (* A019298 *)

LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, 2, 8, 22}, 40]

CROSSREFS

Cf. A211795.

Sequence in context: A137101 A284922 A212970 * A094533 A006696 A094939

Adjacent sequences:  A212680 A212681 A212682 * A212684 A212685 A212686

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 24 2012

STATUS

approved

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Last modified August 3 20:08 EDT 2020. Contains 336201 sequences. (Running on oeis4.)