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A212905 Number of (w,x,y,z) with all terms in {0,...,n} and |w-x|+|x-y+|y-z|=2n. 2
1, 6, 16, 26, 42, 58, 82, 106, 140, 174, 220, 266, 326, 386, 462, 538, 632, 726, 840, 954, 1090, 1226, 1386, 1546, 1732, 1918, 2132, 2346, 2590, 2834, 3110, 3386, 3696, 4006, 4352, 4698, 5082, 5466, 5890, 6314, 6780, 7246, 7756, 8266, 8822 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For a guide to related sequences, see A211795.

LINKS

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

FORMULA

a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6) for n>=1.

G.f.: f(x)/g(x), where f(x)=1 + 4*x + 3*x^2 - 8*x^3 - 3*x^4 + 4*x^5 + x^6 and g(x)=((1-x)^4)*(1+x)^2.

MATHEMATICA

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

(Do[If[Abs[w - x] + Abs[x - y] + Abs[y - z] == 2 n, s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}, {z, 0, n}]; s)]];

m = Map[t[#] &, Range[0, 40]]   (* A212905 *)

CROSSREFS

Cf. A211795.

Sequence in context: A232491 A191157 A222180 * A191117 A265389 A320693

Adjacent sequences:  A212902 A212903 A212904 * A212906 A212907 A212908

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 01 2012

STATUS

approved

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Last modified June 16 11:12 EDT 2019. Contains 324152 sequences. (Running on oeis4.)