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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A051877 Partial sums of A051740. 4
1, 12, 57, 182, 462, 1008, 1974, 3564, 6039, 9724, 15015, 22386, 32396, 45696, 63036, 85272, 113373, 148428, 191653, 244398, 308154, 384560, 475410, 582660, 708435, 855036, 1024947, 1220842, 1445592, 1702272, 1994168, 2324784, 2697849, 3117324, 3587409 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of triangular numbers (A000217) and enneagonal numbers (A001106). [Bruno Berselli, Jul 21 2015]

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.

LINKS

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

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = C(n+4, 4)*(7n+5)/5.

G.f.: (1+6*x)/(1-x)^6.

From Wesley Ivan Hurt, May 02 2015: (Start)

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).

a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120. (End)

MAPLE

A051877:=n->binomial(n+4, 4)*(7*n+5)/5: seq(A051877(n), n=0..50); # Wesley Ivan Hurt, May 02 2015

MATHEMATICA

f[n_]:=7*n+1; s1=s2=s3=s4=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst, s4], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 25 2009 *)

Table[(n + 1) (n + 2) (n + 3) (n + 4) (7 n + 5) / 120, {n, 0, 50}] (* Vincenzo Librandi, May 03 2015 *)

PROG

(MAGMA) [(n+1)*(n+2)*(n+3)*(n+4)*(7*n+5)/120 : n in [0..50]]; // Wesley Ivan Hurt, May 02 2015

CROSSREFS

Cf. A051740; A000217, A001106.

Cf. A093564 ((7, 1) Pascal, column m=5).

Sequence in context: A212682 A212134 A071270 * A212065 A121693 A190297

Adjacent sequences:  A051874 A051875 A051876 * A051878 A051879 A051880

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, Dec 14 1999

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 20 16:14 EST 2018. Contains 299380 sequences. (Running on oeis4.)