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!)
A061224 a(n) = n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5. 1
260, 1114, 3412, 8474, 18244, 35410, 63524, 107122, 171844, 264554, 393460, 568234, 800132, 1102114, 1488964, 1977410, 2586244, 3336442, 4251284, 5356474, 6680260, 8253554, 10110052, 12286354, 14822084, 17760010, 21146164, 25029962 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
G.f.: 2*(130 - 223*x + 314*x^2 - 244*x^3 + 100*x^4 - 17*x^5)/(1-x)^6. - Bruno Berselli, Aug 05 2011
E.g.f.: exp(x)*(260 + 854*x + 722*x^2 + 220*x^3 + 26*x^4 + x^5). - Stefano Spezia, Nov 02 2018
EXAMPLE
a(1) = 1 + 2^3 + 3^4 + 4^5 = 1 + 8 + 81 + 1024 = 1114.
MAPLE
seq(n^2+(n+1)^3+(n+2)^4+(n+3)^5, n=0..30); # Muniru A Asiru, Nov 02 2018
MATHEMATICA
Table[n^2 +(n+1)^3 +(n+2)^4 +(n+3)^5, {n, 0, 30}] (* G. C. Greubel, Nov 02 2018 *)
CoefficientList[Series[E^x (260 + 854 x + 722 x^2 + 220 x^3 + 26 x^4 + x^5), {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* Stefano Spezia, Nov 02 2018 *)
Table[260+440 n+298 n^2+99 n^3+16 n^4+n^5, {n, 0, 30}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {260, 1114, 3412, 8474, 18244, 35410}, 30] (* Harvey P. Dale, Nov 14 2022 *)
PROG
(Magma) [n^2 + (n + 1)^3 + (n + 2)^4 + (n + 3)^5: n in [0..30]]; // Vincenzo Librandi, Aug 05 2011
(PARI) vector(30, n, n--; n^2 +(n+1)^3 +(n+2)^4 +(n+3)^5) \\ G. C. Greubel, Nov 02 2018
(GAP) List([0..30], n->n^2+(n+1)^3+(n+2)^4+(n+3)^5); # Muniru A Asiru, Nov 02 2018
CROSSREFS
Cf. A027621.
Sequence in context: A202585 A037219 A290040 * A108109 A235905 A287923
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, May 31 2001
EXTENSIONS
Offset changed from 1 to 0 by Vincenzo Librandi, Aug 05 2011
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 February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)