login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A212511 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y>=3z. 2
0, 0, 0, 7, 24, 57, 135, 259, 432, 732, 1125, 1638, 2376, 3302, 4410, 5915, 7680, 9765, 12393, 15447, 18900, 23170, 27951, 33348, 39744, 46900, 54756, 63999, 74088, 85185, 97875, 111755, 126720, 143792, 162129, 181962, 204120, 227994, 253422, 281827, 312000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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^3*(7 +24*x +43*x^2 +73*x^3 +104*x^4 +100*x^5 +97*x^6 +92*x^7 +61*x^8 +30*x^9 +14*x^10 +3*x^11) / ((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]] (* A212511 *)

PROG

(PARI) concat(vector(3), Vec(x^3*(7 +24*x +43*x^2 +73*x^3 +104*x^4 +100*x^5 +97*x^6 +92*x^7 +61*x^8 +30*x^9 +14*x^10 +3*x^11) / ((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, A212509, A212510.

Sequence in context: A159225 A146298 A079671 * A100454 A081436 A024205

Adjacent sequences: A212508 A212509 A212510 * A212512 A212513 A212514

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 20 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 06:18 EST 2022. Contains 358431 sequences. (Running on oeis4.)