login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A212507 Number of (w,x,y,z) with all terms in {1,...,n} and w<2x and y<=2z. 2
0, 1, 12, 56, 168, 399, 810, 1480, 2496, 3965, 6000, 8736, 12312, 16891, 22638, 29744, 38400, 48825, 61236, 75880, 93000, 112871, 135762, 161976, 191808, 225589, 263640, 306320, 353976, 406995, 465750, 530656, 602112, 680561, 766428 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

For a guide to related sequences, see A211795.

LINKS

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).

FORMULA

a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).

G.f.: x*(1+2*x)*(1+7*x+7*x^2+3*x^3)/((1+x)^2*(1-x)^5). [Bruno Berselli, May 31 2012]

a(n) = (2*n*(9*n^3+6*n^2+1)-(2*n-1)*(-1)^n-1)/32. [Bruno Berselli, May 31 2012]

a(n) = A006578(n) * A077043(n). - Alois P. Heinz, May 31 2012

MATHEMATICA

t = Compile[{{n, _Integer}}, Module[{s = 0},

(Do[If[w < 2 x && y <= 2 z, s = s + 1],

{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];

Map[t[#] &, Range[0, 40]]   (* A212507 *)

CoefficientList[Series[x (1 + 2 x) (1 + 7 x + 7 x^2 + 3 x^3)/((1 + x)^2 (1 - x)^5), {x, 0, 34}], x] (* Bruno Berselli, May 31 2012 *)

PROG

(MAGMA) [(2*n*(9*n^3+6*n^2+1)-(2*n-1)*(-1)^n-1)/32: n in [0..34]]; // Bruno Berselli, May 31 2012

CROSSREFS

Cf. A211795.

Sequence in context: A035005 A001386 A046998 * A212508 A331771 A009430

Adjacent sequences:  A212504 A212505 A212506 * A212508 A212509 A212510

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 19 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)