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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101091 Fourth partial sums of fourth powers (A000583). 10
1, 20, 155, 760, 2814, 8592, 22770, 54120, 117975, 239668, 459173, 837200, 1463020, 2464320, 4019412, 6372144, 9849885, 14884980, 22040095, 32037896, 45795530, 64464400, 89475750, 122592600, 165968595, 222214356, 294471945, 386498080 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..28.

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

FORMULA

a(n) = n*(1 + n)*(2 + n)^2*(3 + n)*(4 + n)*(-1 + 3*n*(4 + n))/5040.

a(1)=1, a(2)=20, a(3)=155, a(4)=760, a(5)=2814, a(6)=8592, a(7)=22770, a(8)=54120, a(9)=117975, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). [Harvey P. Dale, Dec 30 2011]

G.f.: x*(1+x)*(1+10*x+x^2)/(1-x)^9. [Colin Barker, Apr 04 2012]

MATHEMATICA

Nest[Accumulate, Range[30]^4, 4] (* or *) LinearRecurrence[ {9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 20, 155, 760, 2814, 8592, 22770, 54120, 117975}, 30] (* Harvey P. Dale, Dec 30 2011 *)

CROSSREFS

Cf. A101090.

Sequence in context: A164605 A000492 A015866 * A120693 A120692 A324948

Adjacent sequences:  A101088 A101089 A101090 * A101092 A101093 A101094

KEYWORD

easy,nonn

AUTHOR

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004

EXTENSIONS

Edited by Ralf Stephan, Dec 16 2004

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 19 23:59 EDT 2019. Contains 327207 sequences. (Running on oeis4.)