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A212564 Number of (w,x,y,z) with all terms in {1,...,n} and w+x>2y+2z. 2
0, 0, 0, 3, 16, 48, 114, 229, 416, 696, 1100, 1655, 2400, 3368, 4606, 6153, 8064, 10384, 13176, 16491, 20400, 24960, 30250, 36333, 43296, 51208, 60164, 70239, 81536, 94136, 108150, 123665, 140800, 159648, 180336, 202963, 227664, 254544, 283746, 315381 (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*(2*n*(3*((-1)^n-1)+(n-2)*n*(7*n-4))-9*(-1)^n+9).

G.f.: x^3*(3+7*x+3*x^2+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]]   (* A212564 *)

PROG

(PARI) concat(vector(3), Vec(x^3*(3+7*x+3*x^2+x^3) / ((1-x)^5*(1+x)^2) + O(x^100))) \\ Colin Barker, Dec 05 2015

CROSSREFS

Cf. A211795.

Sequence in context: A296947 A255211 A172482 * A222843 A004320 A089363

Adjacent sequences:  A212561 A212562 A212563 * A212565 A212566 A212567

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 21 2012

STATUS

approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)