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A212982 Number of (w,x,y) with all terms in {0,...,n} and w<x+y and x<=y. 2
0, 3, 11, 27, 53, 92, 146, 218, 310, 425, 565, 733, 931, 1162, 1428, 1732, 2076, 2463, 2895, 3375, 3905, 4488, 5126, 5822, 6578, 7397, 8281, 9233, 10255, 11350, 12520, 13768, 15096, 16507, 18003, 19587, 21261, 23028, 24890, 26850, 28910, 31073, 33341, 35717 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For a guide to related sequences, see A212959.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

FORMULA

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

G.f.: f(x)/g(x), where f(x)=3*x + 2*x^2 and g(x)=(1+x)*(1-x)^4.

From Colin Barker, Jan 28 2016: (Start)

a(n) = (20*n^3+66*n^2+52*n-3*(-1)^n+3)/48.

a(n) = (10*n^3+33*n^2+26*n)/24 for n even.

a(n) = (10*n^3+33*n^2+26*n+3)/24 for n odd.

(End)

MATHEMATICA

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

(Do[If[w < x + y && x <= y, s = s + 1],

{w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]];

m = Map[t[#] &, Range[0, 60]]   (* A212982 *)

PROG

(PARI) concat(0, Vec(x*(3+2*x)/((1-x)^4*(1+x)) + O(x^100))) \\ Colin Barker, Jan 28 2016

CROSSREFS

Cf. A212959.

Sequence in context: A186301 A170945 A164897 * A164845 A024194 A011941

Adjacent sequences:  A212979 A212980 A212981 * A212983 A212984 A212985

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 04 2012

STATUS

approved

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Last modified May 8 08:30 EDT 2021. Contains 343660 sequences. (Running on oeis4.)