login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A162148 a(n) = n*(n+1)*(5*n+7)/6. 6
0, 4, 17, 44, 90, 160, 259, 392, 564, 780, 1045, 1364, 1742, 2184, 2695, 3280, 3944, 4692, 5529, 6460, 7490, 8624, 9867, 11224, 12700, 14300, 16029, 17892, 19894, 22040, 24335, 26784, 29392, 32164, 35105, 38220, 41514, 44992, 48659, 52520, 56580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A147875.

Equals the fourth right hand column of A175136 for n>=1. - Johannes W. Meijer, May 06 2011

a(n) is the number of triples (w,x,y) havingt all terms in {0,...,n} and x+y>w. - Clark Kimberling, Jun 14 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

FORMULA

a(n) = A162147(n)+A000217(n).

From Johannes W. Meijer, May 06 2011: (Start)

G.f.: x*(4+x)/(x-1)^4

a(n) = 4*binomial(n+2,3)+binomial(n+1,3)

a(n) = A091894(3,0)*binomial(n+2,3)+ A091894(3,1)*binomial(n+1,3). (End)

a(n) = (n+1)*A000290(n+1) - sum(A000217(i), i=1..n+1).

a(0)=0, a(1)=4, a(2)=17, a(3)=44, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, May 20 2014

MATHEMATICA

f[n_]:=5*n+4; s1=s2=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; AppendTo[lst, s2], {n, 0, 6!}]; lst

Table[(n(n+1)(5n+7))/6, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 4, 17, 44}, 50] (* Harvey P. Dale, May 20 2014 *)

PROG

(MAGMA) [n*(n+1)*(5*n+7)/6: n in [0..50]]; // Vincenzo Librandi, May 07 2011

(PARI) a(n)=n*(n+1)*(5*n+7)/6 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A033994, A002413, A016061, A006331, A002412, A162147, A175136, A190048, A190049, A254407.

Related to A000292 and A091894.

Sequence in context: A275815 A018973 A212575 * A166781 A147656 A095667

Adjacent sequences:  A162145 A162146 A162147 * A162149 A162150 A162151

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jun 25 2009

EXTENSIONS

Definition rephrased by R. J. Mathar, Jun 27 2009

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 February 16 09:19 EST 2019. Contains 320160 sequences. (Running on oeis4.)