A058373 a(n) = (1/6)*(2*n - 3)*(n + 2)*(n + 1).

0, 0, -1, -1, 2, 10, 25, 49, 84, 132, 195, 275, 374, 494, 637, 805, 1000, 1224, 1479, 1767, 2090, 2450, 2849, 3289, 3772, 4300, 4875, 5499, 6174, 6902, 7685, 8525, 9424, 10384, 11407, 12495, 13650, 14874, 16169, 17537, 18980, 20500, 22099

Offset

-2,5

Comments

For n>=0, real parts of sum_(k=0)^n (k+i)^2, where i=sqrt(-1). [Bruno Berselli, Jan 24 2014]

Links

Michael De Vlieger, Table of n, a(n) for n = -2..10000

Francesco Toppan, Z_2 X Z_2-graded parastatistics in multiparticle quantum Hamiltonians, arXiv:2008.11554 [hep-th], 2020.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 2*C(n+2,3) - C(n+2,2). - Zerinvary Lajos, Nov 25 2006

Maple

seq((2*n-3)*(n+2)*(n+1)/6, n=-2..40);

Mathematica

s=0; lst={0, s}; Do[s+=n^2-1; AppendTo[lst, s], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)
Table[((2n-3)(n+2)(n+1))/6, {n, -2, 40}] (* Harvey P. Dale, Apr 21 2019 *)

Crossrefs

Cf. A236377: real part of sum_(k=0)^n (k + i^k)^2, i=sqrt(-1). [Bruno Berselli, Jan 25 2014]

Sequence in context: A345695 A336958 A305600 * A167386 A027719 A254709

Adjacent sequences: A058370 A058371 A058372 * A058374 A058375 A058376

Keyword

sign,easy

Author

N. J. A. Sloane, Dec 18 2000

Status

approved