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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A129863 Sums of three consecutive pentagonal numbers. 4
6, 18, 39, 69, 108, 156, 213, 279, 354, 438, 531, 633, 744, 864, 993, 1131, 1278, 1434, 1599, 1773, 1956, 2148, 2349, 2559, 2778, 3006, 3243, 3489, 3744, 4008, 4281, 4563, 4854, 5154, 5463, 5781, 6108, 6444, 6789, 7143, 7506, 7878, 8259, 8649, 9048, 9456 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Arises in pentagonal number analog to A129803, Triangular numbers that are the sum of three consecutive triangular numbers. What are the pentagonal numbers which are the sum of three consecutive pentagonal numbers?

LINKS

Table of n, a(n) for n=1..46.

FORMULA

a(n) = P(n) + P(n+1) + P(n+2) where P(n) = A000326(n) = n(3n-1)/2.

a(n) = P(n) + P(n+1) + P(n+2) where P(n) = A000326(n) = n(3n-1)/2. For n = 0, 1, 2, ... a(n+1) = (9/2)*(n^2) + (15/2)*n + 6.

a(n) = (3n^2+5n+4)*(3/2). - Stefan Steinerberger, May 27 2007

G.f.: 3*x*(2+x^2)/(1-x)^3. - Colin Barker, Feb 13 2012

EXAMPLE

a(1) = 6 = A000326(0) + A000326(1) + A000326(2) = 0 + 1 + 5.

a(2) = 18 = A000326(1) + A000326(2) + A000326(3) = 1 + 5 + 12.

MATHEMATICA

Table[(3/2)*(4 + 5*n + 3*n^2), {n, 0, 100}] (* Stefan Steinerberger, May 27 2007 *)

CROSSREFS

Cf. A000326, A007667, A034961, A129803.

Sequence in context: A270081 A261651 A270215 * A272014 A272453 A271252

Adjacent sequences:  A129860 A129861 A129862 * A129864 A129865 A129866

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 23 2007, May 24 2007

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 March 29 13:17 EDT 2017. Contains 284270 sequences.