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A212565 Number of (w,x,y,z) with all terms in {1,...,n} and w+x>=2y+2z. 2
0, 0, 1, 8, 28, 74, 159, 304, 528, 860, 1325, 1960, 2796, 3878, 5243, 6944, 9024, 11544, 14553, 18120, 22300, 27170, 32791, 39248, 46608, 54964, 64389, 74984, 86828, 100030, 114675, 130880, 148736, 168368, 189873, 213384, 239004, 266874, 297103, 329840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

For a guide to related sequences, see A211795.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).

FORMULA

a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).

From Colin Barker, Dec 05 2015: (Start)

a(n) = 1/96*(14*n^4-12*n^3-8*n^2-6*((-1)^n-1)*n+3*((-1)^n-1)).

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

(End)

MATHEMATICA

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

(Do[If[w + x >= 2 y + 2 z, s = s + 1],

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

Map[t[#] &, Range[0, 40]]   (* A212565 *)

PROG

(PARI) concat([0, 0], Vec(x^2*(1+5*x+5*x^2+3*x^3)/((1-x)^5*(1+x)^2) + O(x^100))) \\ Colin Barker, Dec 05 2015

CROSSREFS

Cf. A211795.

Sequence in context: A153976 A105636 A102665 * A209408 A316214 A134638

Adjacent sequences:  A212562 A212563 A212564 * A212566 A212567 A212568

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 21 2012

STATUS

approved

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Last modified February 20 06:26 EST 2019. Contains 320332 sequences. (Running on oeis4.)