A131179 a(n) = if n mod 2 == 0 then n*(n+1)/2, otherwise (n-1)*n/2 + 1.

0, 1, 3, 4, 10, 11, 21, 22, 36, 37, 55, 56, 78, 79, 105, 106, 136, 137, 171, 172, 210, 211, 253, 254, 300, 301, 351, 352, 406, 407, 465, 466, 528, 529, 595, 596, 666, 667, 741, 742, 820, 821, 903, 904, 990, 991, 1081, 1082, 1176, 1177, 1275, 1276, 1378, 1379, 1485, 1486

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

G.f.: -x*(1+2*x-x^2+2*x^3) / ( (1+x)^2*(x-1)^3 ). - R. J. Mathar, Sep 05 2012

a(n) = ( n^2+1+(n-1)*(-1)^n )/2. - Luce ETIENNE, Aug 19 2014

Mathematica

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 3, 4, 10}, 60] (* Jean-François Alcover, Feb 12 2016 *)

Prog

(Haskell)
a131179 n = (n + 1 - m) * n' + m  where (n', m) = divMod n 2
-- Reinhard Zumkeller, Oct 12 2013
(Magma) [(n^2+1+(n-1)*(-1)^n )/2: n in [0..60]]; // Vincenzo Librandi, Feb 12 2016
(Python)
def A131179(n): return n*(n+1)//2 + (1-n)*(n % 2) # Chai Wah Wu, May 24 2022

Crossrefs

Cf. A128918.

Sequence in context: A327300 A047341 A091910 * A079353 A242654 A243681

Adjacent sequences: A131176 A131177 A131178 * A131180 A131181 A131182

Keyword

nonn,easy

Author

Philippe LALLOUET, Sep 16 2007

Status

approved