A211541 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w=3x-4y.

0, 0, 1, 1, 3, 3, 6, 7, 11, 11, 17, 18, 24, 25, 33, 34, 43, 44, 54, 56, 67, 68, 81, 83, 96, 98, 113, 115, 131, 133, 150, 153, 171, 173, 193, 196, 216, 219, 241, 244, 267, 270, 294, 298, 323, 326, 353, 357, 384, 388, 417, 421, 451, 455, 486, 491, 523, 527

Offset

0,5

Comments

For a guide to related sequences, see A211422.

Links

Bo Gyu Jeong, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6)-a(n-7)+a(n-9).

G.f.: x^2*(1+x+2*x^2+x^3+x^4+x^5+x^6)/((1+x^2)*(1+x+x^2)*(1+x)^2*(1-x)^3). [Bruno Berselli, Jun 15 2012]

Mathematica

t[n_] := t[n] = Flatten[Table[2 w - 3 x + 4 y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 80}]  (* A211541 *)
FindLinearRecurrence[t]

Crossrefs

Cf. A211422.

Sequence in context: A270060 A350636 A078565 * A026926 A332557 A083751

Adjacent sequences: A211538 A211539 A211540 * A211542 A211543 A211544

Keyword

nonn,easy

Author

Clark Kimberling, Apr 15 2012

Status

approved