|
Search: id:A062393
|
|
|
| A062393 |
|
a(n)=n^5-(n-1)^5+(n-2)^5-....0^5. |
|
+0
5
|
|
| 0, 1, 31, 212, 812, 2313, 5463, 11344, 21424, 37625, 62375, 98676, 150156, 221137, 316687, 442688, 605888, 813969, 1075599, 1400500, 1799500, 2284601, 2869031, 3567312, 4395312, 5370313, 6511063, 7837844, 9372524, 11138625, 13161375
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Contribution from Peter Luschny (peter(AT)luschny.de), Jul 12 2009: (Start)
The general formula for alternating sums of powers is in terms of the Swiss-Knife polynomials P(n,x) A153641 2^(-n-1)(P(n,1)-(-1)^k P(n,2k+1)). Thus
a(k) = |2^(-6)(P(5,1)-(-1)^k P(5,2k+1))|. (End)
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=0,...,1000
|
|
FORMULA
|
a(n) =(2*n^5+5*n^4-5*n^2+1-(-1)^n)/4 =n^5-a(n-1).
|
|
MAPLE
|
a := n -> (1-(-1)^n+n^2*(n^2*(2*n+5)-5))/4; [From Peter Luschny (peter(AT)luschny.de), Jul 12 2009]
|
|
MATHEMATICA
|
k=0; lst={k}; Do[k=n^5-k; AppendTo[lst, k], {n, 1, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
|
|
PROGRAM
|
(PARI) { a=0; for (n=0, 1000, write("b062393.txt", n, " ", a=n^5 - a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 07 2009]
|
|
CROSSREFS
|
Cf. A000539, A000584. A062392 provides the result for 4th powers, A011934 for cubes, A000217 for squares, A001057 (unsigned) for nonnegative integers, A000035 (offset) for 0th powers.
Sequence in context: A090027 A164784 A121616 this_sequence A042874 A001136 A142939
Adjacent sequences: A062390 A062391 A062392 this_sequence A062394 A062395 A062396
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Henry Bottomley (se16(AT)btinternet.com), Jun 21 2001
|
|
|
Search completed in 0.002 seconds
|
