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A212976 Number of (w,x,y) with all terms in {0,...,n} and odd range. 3
0, 6, 12, 36, 60, 114, 168, 264, 360, 510, 660, 876, 1092, 1386, 1680, 2064, 2448, 2934, 3420, 4020, 4620, 5346, 6072, 6936, 7800, 8814, 9828, 11004, 12180, 13530, 14880, 16416, 17952, 19686, 21420, 23364, 25308, 27474, 29640, 32040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) + A212975(n) = (n+1)^3. Six divides every term.

For a guide to related sequences, see A212959.

LINKS

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

FORMULA

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

G.f.: f(x)/g(x), where f(x) = 6*x*(1 + x^2) and g(x) = ((1-x)^4)*(1+x)^2.

a(n+1) = 6*A005993(n). [Bruno Berselli, Jun 15 2012]

MATHEMATICA

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

(Do[If[Mod[Max[w, x, y] - Min[w, x, y], 2] == 1,

   s = s + 1],

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

m = Map[t[#] &, Range[0, 60]]   (* A212976 *)

m/6  (* A005993 except for initial 0 *)

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 6, 12, 36, 60, 114}, 40] (* Harvey P. Dale, Jan 21 2017 *)

CROSSREFS

Cf. A005993, A212959, A212975.

Sequence in context: A127845 A306899 A096932 * A176681 A064476 A324483

Adjacent sequences:  A212973 A212974 A212975 * A212977 A212978 A212979

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 03 2012

STATUS

approved

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Last modified August 18 22:26 EDT 2019. Contains 326109 sequences. (Running on oeis4.)