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A055999 a(n) = n*(n+7)/2. 25
0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, 1122, 1170, 1219, 1269, 1320, 1372, 1425, 1479 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A126890(n,3) for n>2. - Reinhard Zumkeller, Dec 30 2006

If X is an n-set and Y a fixed (n-4)-subset of X then a(n-3) is equal to the number of 2-subsets of X intersecting Y. - Milan Janjic, Aug 15 2007

Numbers m >= 0 such that 8m+49 is a square. - Bruce J. Nicholson, Jul 28 2017

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 193.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Milan Janjic, Two Enumerative Functions

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

FORMULA

G.f.: x(4-3x)/(1-x)^3.

a(n) = C(n,2) - 3*n, n>=7. - Zerinvary Lajos, Nov 25 2006

Equals A028563/2. - Zerinvary Lajos, Feb 12 2007

If we define f(n,i,a) = sum_{k=0..n-i} binomial(n,k)*stirling1(n-k,i)*product_{j=0..k-1} (-a-j), then a(n) = -f(n,n-1,4), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = n + a(n-1) + 3 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010

a(n) = Sum_{k=1..n} (k+3). - Gary Detlefs, Aug 10 2010

Sum_{n>=1} 1/a(n) = 363/490. - R. J. Mathar, Jul 14 2012

a(n) = 4n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

a(n) = Sum_{i=4..n+3} i. - Wesley Ivan Hurt, Jun 28 2013

E.g.f.: (1/2)*x*(x+8)*exp(x). - G. C. Greubel, Jul 13 2017

MAPLE

a:=n->sum(floor(k+2*n/(k+n)), k=3..n): seq(a(n), n=2..53); # Zerinvary Lajos, Oct 01 2006

[seq(binomial(n, 2)-3*n, n=7..58)]; # Zerinvary Lajos, Nov 25 2006

a:=n->sum(numer (k/(k+3)), k=4..n): seq(a(n), n=3..54); # Zerinvary Lajos, May 31 2008

with (combinat):seq((fibonacci(3, n)+n-13)/2, n=3..54); # Zerinvary Lajos, Jun 07 2008

MATHEMATICA

lst={}; Do[AppendTo[lst, n*(n+7)/2], {n, 0, 5!}]; lst ...and/or... s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 3, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2008 *)

Table[n*(n + 7)/2, {n, 0, 50}] (* G. C. Greubel, Jul 13 2017 *)

PROG

(PARI) a(n)=n*(n+7)/2 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Equals A000217(n+3) - 6.

Cf. A000096, A055998, A074171, A056000, A001477, A002522, A028563, A126890.

Third column (m=2) of (1, 4)-Pascal triangle A095666.

Sequence in context: A073046 A066495 A134227 * A022945 A022948 A022443

Adjacent sequences:  A055996 A055997 A055998 * A056000 A056001 A056002

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jun 16 2000

EXTENSIONS

More terms from James A. Sellers, Jul 04 2000

STATUS

approved

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.