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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227316 a(n) = n(n+1) if n == 0 or 1 (mod 4), otherwise a(n) = n(n+1)/2. 3
0, 2, 3, 6, 20, 30, 21, 28, 72, 90, 55, 66, 156, 182, 105, 120, 272, 306, 171, 190, 420, 462, 253, 276, 600, 650, 351, 378, 812, 870, 465, 496, 1056, 1122, 595, 630, 1332, 1406, 741, 780, 1640, 1722, 903, 946, 1980, 2070, 1081, 1128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1).

FORMULA

a(n) = A130658(n+2)*A000217(n), a(-n-1) = A130658(n)*A000217(n).

a(2n) = A169642(n), a(2n+1) = 2*(2*n+1)*A026741(n+1).

a(n) = A176743(n-2)*A176743(n-1).

a(n) = A177002(n+2)*A064038(n+1).

a(n) = 3*a(n-1) -6*a(n-2) +10*a(n-3) -12*a(n-4) +12*a(n-5) -10*(n-6) +6*(n-7) -3*a(n-8) +a(n-9) = 3*a(n-4) -3*a(n-8) +a(n-12).

G.f.: x*(2-3*x+9*x^2+3*x^5+x^6)/((1-x)^3*(1+x^2)^3). [Bruno Berselli, Jul 10 2013]

a(n) = (3+(-1)^floor(n/2))*n*(n+1)/4. [Bruno Berselli, Jul 10 2013]

EXAMPLE

a(0)=2*0=0, a(1)=2*1=2, a(2)=1*3=3, a(3)=1*6=6, a(4)=2*10=20.

MATHEMATICA

a[n_] := n*(n+1)/4*GCD[n-1, 4]*GCD[n, 4]; Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Jul 10 2013 *)

Table[If[Mod[n, 4]<2, n(n+1), (n(n+1))/2], {n, 0, 50}] (* or *) LinearRecurrence[ {3, -6, 10, -12, 12, -10, 6, -3, 1}, {0, 2, 3, 6, 20, 30, 21, 28, 72}, 50] (* Harvey P. Dale, Aug 26 2016 *)

PROG

(MAGMA) [(3+(-1)^Floor(n/2))*n*(n+1)/4: n in [0..50]]; // Bruno Berselli, Jul 10 2013

CROSSREFS

Cf. A000217, A002378, A130658, A169642 (first bisection), A176743, A109043, A227380.

Sequence in context: A259456 A254441 A173744 * A176806 A168268 A277876

Adjacent sequences:  A227313 A227314 A227315 * A227317 A227318 A227319

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jul 06 2013

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 January 18 11:33 EST 2019. Contains 319271 sequences. (Running on oeis4.)