The On-Line Encyclopedia of Integer Sequences (OEIS)

A211440 revision #7

A211440

Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and 2w+3x+3y=0.

1, 3, 5, 17, 23, 29, 53, 63, 73, 109, 123, 137, 185, 203, 221, 281, 303, 325, 397, 423, 449, 533, 563, 593, 689, 723, 757, 865, 903, 941, 1061, 1103, 1145, 1277, 1323, 1369, 1513, 1563, 1613, 1769, 1823, 1877, 2045, 2103, 2161, 2341, 2403, 2465

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OFFSET

0,2

COMMENTS

For a guide to related sequences, see A211422.

LINKS

Table of n, a(n) for n=0..47.

FORMULA

Conjectures from Colin Barker, May 15 2017: (Start)

G.f.: (1 + 3*x + x^2)*(1 - x + 4*x^2 - x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)^2).

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

(End)

MATHEMATICA

t[n_] := t[n] = Flatten[Table[2 w + 3 x + 3 y, {w, -n, n}, {x, -n, n}, {y, -n, n}]]

c[n_] := Count[t[n], 0]

t = Table[c[n], {n, 0, 30}] (* A211440 *)

(t - 1)/2 (* integers *)

CROSSREFS

Cf. A211422.

Sequence in context: A153417 A069687 A079017 * A100564 A231232 A154608

Adjacent sequences: A211437 A211438 A211439 * A211441 A211442 A211443

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 11 2012

STATUS

approved