A339573 a(n) = floor(n*(n+1)/6) - 1.

0, 1, 2, 4, 6, 8, 11, 14, 17, 21, 25, 29, 34, 39, 44, 50, 56, 62, 69, 76, 83, 91, 99, 107, 116, 125, 134, 144, 154, 164, 175, 186, 197, 209, 221, 233, 246, 259, 272, 286, 300, 314, 329, 344, 359, 375, 391, 407, 424, 441, 458, 476, 494, 512, 531, 550, 569, 589, 609, 629, 650, 671, 692

Offset

2,3

Comments

a(n) = A001840(n-1)-1.

Links

Harvey P. Dale, Table of n, a(n) for n = 2..1000

Bernhard Ganter, Notes on Integer Partitions, Technische Universität Dresden (2020); See Prop. 3.

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Formula

G.f.: x^3*(-1-x^2+x^3) / ( (1+x+x^2)*(x-1)^3 ). - R. J. Mathar, Jan 14 2021

Mathematica

Table[Floor[n (n + 1)/6] - 1, {n, 2, 80}] (* Robert P. P. McKone, Dec 19 2020 *)
LinearRecurrence[{2, -1, 1, -2, 1}, {0, 1, 2, 4, 6}, 90] (* Harvey P. Dale, Feb 15 2026 *)

Prog

(Python)
def A339573(n):
    return n*(n+1)//6-1 # Chai Wah Wu, Dec 10 2020

Crossrefs

Cf. A001840.

Sequence in context: A237886 A212555 A328787 * A060655 A117490 A359275

Adjacent sequences: A339570 A339571 A339572 * A339574 A339575 A339576

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 10 2020

Status

approved