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A212675 Number of (w,x,y,z) with all terms in {1,...,n} and  w>=|x-y|+|y-z|. 2
0, 1, 14, 57, 158, 353, 688, 1217, 2004, 3121, 4650, 6681, 9314, 12657, 16828, 21953, 28168, 35617, 44454, 54841, 66950, 80961, 97064, 115457, 136348, 159953, 186498, 216217, 249354, 286161, 326900, 371841, 421264, 475457, 534718 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)+A212568(n)=n^4.

For a guide to related sequences, see A211795.

LINKS

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (4, -5, 0, 5, -4, 1).

FORMULA

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

G.f.: (x + 10*x^2 + 6*x^3 + x^5)/(1 - 4 x + 5 x^2 - 5 x^4 + 4 x^5 + x^6)

MATHEMATICA

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

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

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

Map[t[#] &, Range[0, 40]]   (* A212675 *)

LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 1, 14, 57, 158, 353}, 40]

CROSSREFS

Cf. A211795.

Sequence in context: A022286 A005915 A211069 * A041376 A063537 A084195

Adjacent sequences:  A212672 A212673 A212674 * A212676 A212677 A212678

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 23 2012

STATUS

approved

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Last modified February 15 20:32 EST 2019. Contains 320138 sequences. (Running on oeis4.)