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A212673 Number of (w,x,y,z) with all terms in {1,...,n}  and w<=|x-y|+|y-z|. 2
0, 0, 8, 46, 152, 378, 792, 1476, 2528, 4060, 6200, 9090, 12888, 17766, 23912, 31528, 40832, 52056, 65448, 81270, 99800, 121330, 146168, 174636, 207072, 243828, 285272, 331786, 383768, 441630, 505800, 576720, 654848, 740656, 834632 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n)+A212674(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.: (8*x^2 + 14*x^3 + 8*x^4)/(1 - 4*x + 5* x^2 - 5*x^4 + 4*x^5 - x^6).

a(n) = (-1+(-1)^n-8*n^2+10*n^4)/16. [Colin Barker, Jun 10 2012]

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]]   (* A212673 *)

%/2  (* integers *)

LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 0, 8, 46, 152, 378}, 40]

CROSSREFS

Cf. A211795.

Sequence in context: A137390 A190048 A034469 * A183392 A258593 A134114

Adjacent sequences:  A212670 A212671 A212672 * A212674 A212675 A212676

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 23 2012

STATUS

approved

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Last modified June 20 11:49 EDT 2021. Contains 345164 sequences. (Running on oeis4.)