A212512 Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y<3z.

0, 1, 16, 64, 196, 462, 930, 1680, 2860, 4485, 6800, 9888, 13908, 19019, 25564, 33440, 43200, 54900, 68796, 85120, 104470, 126511, 152218, 181560, 214896, 252525, 295360, 342720, 396116, 455370, 520950, 593216, 673456, 760529, 856596, 961272, 1075140

Offset

0,3

Comments

For a guide to related sequences, see A211795.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)+2*a(n-7)-2*a(n-9)+4*a(n-11)+a(n-12)-2*a(n-13)-2*a(n-14)+a(n-16).

G.f.: x*(1 +16*x +62*x^2 +162*x^3 +303*x^4 +430*x^5 +492*x^6 +526*x^7 +479*x^8 +372*x^9 +238*x^10 +118*x^11 +35*x^12 +6*x^13) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3). - Colin Barker, Dec 18 2015

Mathematica

t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w <= 2 x && y < 3 z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 50]]   (* A212512 *)

Prog

(PARI) concat(0, Vec(x*(1 +16*x +62*x^2 +162*x^3 +303*x^4 +430*x^5 +492*x^6 +526*x^7 +479*x^8 +372*x^9 +238*x^10 +118*x^11 +35*x^12 +6*x^13) / ((1 -x)^5*(1 +x)^3*(1 -x +x^2)*(1 +x +x^2)^3) + O(x^60))) \\ Colin Barker, Dec 18 2015

Crossrefs

Cf. A211795, A212508.

Sequence in context: A306057 A059165 A212506 * A317235 A255661 A073718

Adjacent sequences: A212509 A212510 A212511 * A212513 A212514 A212515

Keyword

nonn,easy

Author

Clark Kimberling, May 20 2012

Status

approved