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A212575 Number of (w,x,y,z) with all terms in {1,...,n} and  2|w-x|=|x-y|+|y-z|. 2
0, 1, 4, 17, 42, 85, 142, 235, 346, 495, 680, 911, 1172, 1505, 1872, 2305, 2798, 3365, 3978, 4699, 5470, 6335, 7284, 8335, 9448, 10705, 12028, 13473, 15026, 16709, 18470, 20411, 22434, 24607, 26912, 29375, 31932, 34705, 37576, 40625, 43830 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For a guide to related sequences, see A211795.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0, 2, 2, -1, -4, -1, 2, 2, 0, -1).

FORMULA

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10).

G.f.: (x + 4*x^2 + 15*x^3 + 32*x^4 + 44*x^5 + 32*x^6 + 15*x^7 + 4*x^8 + x^9)/(1 - 2*x^2 - 2*x^3 + x^4 + 4*x^5 + x^6 - 2*x^7 - 2*x^8 + x^10)

MATHEMATICA

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

(Do[If[2 Abs[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]]   (* A212575 *)

LinearRecurrence[{0, 2, 2, -1, -4, -1, 2, 2, 0, -1}, {0, 1, 4, 17, 42, 85, 142, 235, 346, 495}, 40]

CROSSREFS

Cf. A211795.

Sequence in context: A145995 A275815 A018973 * A162148 A166781 A147656

Adjacent sequences:  A212572 A212573 A212574 * A212576 A212577 A212578

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 22 2012

STATUS

approved

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Last modified November 14 20:11 EST 2019. Contains 329129 sequences. (Running on oeis4.)