login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A264851 a(n) = n*(n + 1)*(n + 2)*(4*n - 3)/6. 2
0, 1, 20, 90, 260, 595, 1176, 2100, 3480, 5445, 8140, 11726, 16380, 22295, 29680, 38760, 49776, 62985, 78660, 97090, 118580, 143451, 172040, 204700, 241800, 283725, 330876, 383670, 442540, 507935, 580320, 660176, 748000, 844305, 949620, 1064490, 1189476 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Partial sums of 18-gonal (or octadecagonal) pyramidal numbers. Therefore, this is the case k=8 of the general formula n*(n + 1)*(n + 2)*(k*n - k + 2)/12, which is related to 2*(k+1)-gonal pyramidal numbers.
LINKS
OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Pyramidal Number
FORMULA
G.f.: x*(1 + 15*x)/(1 - x)^5.
a(n) = Sum_{k = 0..n} A172078(k).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Nov 27 2015
MATHEMATICA
Table[n (n + 1) (n + 2) (4 n - 3)/6, {n, 0, 50}]
PROG
(Magma) [n*(n + 1)*(n + 2)*(4*n - 3)/6: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015
(PARI) a(n)=n*(n+1)*(n+2)*(4*n-3)/6 \\ Charles R Greathouse IV, Jul 26 2016
CROSSREFS
Cf. A172078.
Cf. similar sequences with formula n*(n+1)*(n+2)*(k*n-k+2)/12 listed in A264850.
Sequence in context: A264302 A220200 A242656 * A345286 A338485 A344334
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Nov 26 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)