OFFSET
0,3
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), with a(0)=1, a(1)=1, a(2)=2, a(3)=6, a(4)=7. - Harvey P. Dale, Mar 31 2012
a(n) = (1/2)*(-1)^n*(n+(-1)^n*((n-2)*n+2)-2). - Harvey P. Dale, Mar 31 2012
G.f.: (1 - x^2 + 4*x^3) / ((1 - x)^3*(1 + x)^2). - Colin Barker, Jan 20 2018
MAPLE
A128918:=n->`if`((n mod 2) = 1, n*(n+1)/2, (n-1)*n/2+1): seq(A128918(n), n=0..100); # Wesley Ivan Hurt, Feb 03 2017
MATHEMATICA
Table[If[OddQ[n], (n(n+1))/2, (n(n-1))/2+1], {n, 0, 60}] (* or *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 1, 2, 6, 7}, 60] (* Harvey P. Dale, Mar 31 2012 *)
CoefficientList[ Series[(-4x^3 + x^2 -1)/((x -1)^3 (x + 1)^2), {x, 0, 55}], x] (* Robert G. Wilson v, Jan 20 2018 *)
PROG
(Haskell)
a128918 n = (n + m - 1) * n' + m * n - m + 1 where (n', m) = divMod n 2
-- Reinhard Zumkeller, Oct 12 2013
(PARI) a(n)=if(n%2, n*(n+1), (n-1)*n+2)/2 \\ Charles R Greathouse IV, Oct 16 2015
(PARI) Vec((1 - x^2 + 4*x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40)) \\ Colin Barker, Jan 20 2018
(Python)
def A128918(n): return n*(n-1)//2 + 1 + (n-1)*(n%2) # Chai Wah Wu, May 24 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 26 2007
STATUS
approved