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A212254 Number of (w,x,y,z) with all terms in {1,...,n} and w=x+2y+3z-n. 2
0, 0, 0, 1, 4, 11, 21, 37, 59, 88, 125, 172, 228, 296, 376, 469, 576, 699, 837, 993, 1167, 1360, 1573, 1808, 2064, 2344, 2648, 2977, 3332, 3715, 4125, 4565, 5035, 5536, 6069, 6636, 7236, 7872, 8544, 9253, 10000, 10787, 11613, 12481, 13391 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

For a guide to related sequences, see A211795.

LINKS

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,-1,0,2,-1).

FORMULA

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

G.f.: x^3*(3*x^2+2*x+1)/((x-1)^4*(x+1)*(x^2+x+1)). [Colin Barker, Oct 07 2012]

MATHEMATICA

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

(Do[If[w == x + 2 y + 3 z - n, s = s + 1],

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

Map[t[#] &, Range[0, 40]]  (*  A212254  *)

(* Peter J. C. Moses, Apr 13 2012 *)

CROSSREFS

Cf. A211795.

Sequence in context: A301173 A110611 A008004 * A301064 A009900 A008230

Adjacent sequences:  A212251 A212252 A212253 * A212255 A212256 A212257

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 15 2012

STATUS

approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)