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A056000 a(n) = n*(n+9)/2. 25
0, 5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 200, 221, 243, 266, 290, 315, 341, 368, 396, 425, 455, 486, 518, 551, 585, 620, 656, 693, 731, 770, 810, 851, 893, 936, 980, 1025, 1071, 1118, 1166, 1215, 1265, 1316, 1368, 1421, 1475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Table of n, a(n) for n=0..50.

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

FORMULA

a(n) = A000217(n+4) - 10.

G.f.: x(5-4x)/(1-x)^3.

From Zerinvary Lajos, Oct 01 2006: (Start)

a(n) = A000096(n) + 3*n.

a(n) = A055999(n) + n.

a(n) = A056115(n) - n.

(End)

a(n) = C(n,2) - 4*n, n>=9. - Zerinvary Lajos, Nov 25 2006

a(n) = A126890(n,4) for n>3. - Reinhard Zumkeller, Dec 30 2006

a(n) = A028569(n)/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-1,5), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = n + a(n-1) + 4. - Vincenzo Librandi, Aug 07 2010

a(n) = sum_{k=1..n} (k+4). - Gary Detlefs, Aug 10 2010

sum_{n>=1} 1/a(n) = 7129/11340. - R. J. Mathar, Jul 14 2012

a(n) = 5n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

MATHEMATICA

lst={}; Do[AppendTo[lst, n*(n+9)/2], {n, 0, 5!}]; lst ...and/or... s=0; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 4, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2008 *)

PROG

(PARI) a(n)=n*(n+9)/2 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000096, A055998, A055999, A001477.

Column m=2 of (1, 5)-Pascal triangle A096940.

Cf. numbers of the form n*(d*n+10-d)/2 indexed in A140090.

Sequence in context: A145005 A004083 A190365 * A080566 A094684 A240438

Adjacent sequences:  A055997 A055998 A055999 * A056001 A056002 A056003

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 March 25 13:25 EDT 2017. Contains 284080 sequences.