A212567 Number of (w,x,y,z) with all terms in {1,...,n} and 2w+2x=3y+3z.

0, 0, 2, 5, 11, 27, 42, 68, 106, 149, 201, 279, 354, 452, 572, 701, 845, 1031, 1212, 1428, 1676, 1937, 2219, 2559, 2892, 3272, 3694, 4133, 4599, 5139, 5670, 6260, 6902, 7565, 8261, 9047, 9822, 10668, 11576, 12509, 13481, 14559, 15624, 16772

Offset: 0

Author

Clark Kimberling, May 22 2012

Keywords

• nonn
• easy

Comments

For a guide to related sequences, see A211795.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,2,2,-1,-4,-1,2,2,0,-1).

Crossrefs

Cf. A211795.

Programs

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[2 w + 2 x == 3 y + 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212567 *)

Maxima

makelist(coeff(taylor(x^2*(2+5*x+7*x^2+13*x^3+12*x^4+5*x^5+x^6+x^7)/((1+x)^2*(1-x)^4*(1+x+x^2)^2), x, 0, n), x, n), n, 0, 43); /* Bruno Berselli, May 06 2012 */

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10).

G.f.: x^2*(2+5*x+7*x^2+13*x^3+12*x^4+5*x^5+x^6+x^7)/((1+x)^2*(1-x)^4*(1+x+x^2)^2). [Bruno Berselli, May 06 2012]