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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A179297 a(n) = n^2 - (n-1)^2 - (n-2)^2 - ... - 1^2. 2
1, 3, 4, 2, -5, -19, -42, -76, -123, -185, -264, -362, -481, -623, -790, -984, -1207, -1461, -1748, -2070, -2429, -2827, -3266, -3748, -4275, -4849, -5472, -6146, -6873, -7655, -8494, -9392, -10351, -11373, -12460, -13614, -14837, -16131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). [From R. J. Mathar, Jul 11 2010]

FORMULA

G.f.: x*(1+x)*(1-2*x)/(1-x)^4. a(n) = -n*(1-9*n+2*n^2)/6 = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). [From R. J. Mathar, Jul 11 2010]

a(0)=1, a(1)=3, a(2)=4, a(3)=2, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) From Harvey P. Dale, Jul 11 2012

Equals -(A000330(n) - AA000326(n) - A000217(n)), for n > 0.  Or by name equals negative of: "Square Pyramidal" - "Pentagonal" - "Triangular". - Richard R. Forberg, Aug 07 2013

EXAMPLE

1^2-0=1,

2^2-1=3,

3^2-2^2-1=4,

4^2-3^2-2^2-1=2,

5^2-4^2-3^2-2^2-1=-5,

...

MATHEMATICA

f[n_]:=Module[{k=n-1, x=n^2}, While[k>0, x-=k^2; k--; ]; x]; lst={}; Do[AppendTo[lst, f[n]], {n, 5!}]; lst

CoefficientList[Series[-(1+x)*(2*x-1)/(x-1)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)

nn=40; Module[{lst=Range[nn]^2, sublst}, Table[sublst=Take[lst, n]; Last[ sublst]- Total[Most[sublst]], {n, nn}]] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {1, 3, 4, 2}, 40] (* Harvey P. Dale, Jul 11 2012 *)

PROG

(MAGMA) I:=[1, 3, 4, 2]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jul 04 2012

CROSSREFS

Cf. A173142.

Sequence in context: A214929 A205152 A162196 * A133620 A154570 A145961

Adjacent sequences:  A179294 A179295 A179296 * A179298 A179299 A179300

KEYWORD

sign,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 09 2010

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 December 3 06:42 EST 2016. Contains 278698 sequences.