A092530 a(0) = 0; for n > 0, a(n) = T(n) + k where T(n) is the n-th triangular number (A000217) and k (see A026741) is the smallest positive number such that a(n) is divisible by n.

0, 2, 4, 9, 12, 20, 24, 35, 40, 54, 60, 77, 84, 104, 112, 135, 144, 170, 180, 209, 220, 252, 264, 299, 312, 350, 364, 405, 420, 464, 480, 527, 544, 594, 612, 665, 684, 740, 760, 819, 840, 902, 924, 989, 1012, 1080, 1104, 1175, 1200, 1274, 1300, 1377, 1404, 1484

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

A. W. Vyawahare and K. M. Purohit, Near pseudo Smarandache function, Smarandache Notions, 14 (2004), 42-61.

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

Formula

a(0) = 0, a(2n) = a(2n-1) + n, a(2n-1) = a(2n-2) + 3n-1. - Amarnath Murthy, Jul 04 2004

From Colin Barker, Feb 03 2019: (Start)

G.f.: x*(2 + 2*x + x^2 - x^3) / ((1 - x)^3*(1 + x)^2).

a(n) = (n*(2 + n)) / 2 for n even.

a(n) = (n*(3 + n)) / 2 for n odd.

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.

(End)

Maple

seq(n*(1+ceil(n/2)), n=0..53); # Zerinvary Lajos and Klaus Brockhaus, Apr 10 2007

Mathematica

{0}~Join~Array[Block[{k = 1}, While[GCD[#1, #2 + k] < #1, k++]; #2 + k] & @@ {#, (#^2 + #)/2} &, 53] (* or *)
CoefficientList[Series[x (2 + 2 x + x^2 - x^3)/((1 - x)^3*(1 + x)^2), {x, 0, 53}], x] (* Michael De Vlieger, Feb 03 2019 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 2, 4, 9, 12}, 60] (* Harvey P. Dale, Sep 21 2024 *)

Prog

(PARI) for(n=0, 53, print1(n*(1+ceil(n/2)), ", ")); \\ Klaus Brockhaus, Apr 10 2007
(PARI) concat(0, Vec(x*(2 + 2*x + x^2 - x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ Colin Barker, Feb 03 2019

Crossrefs

Equals A000217 + A026741.

Sequence in context: A283147 A111302 A241200 * A154891 A282456 A176472

Adjacent sequences: A092527 A092528 A092529 * A092531 A092532 A092533

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 08 2004

Status

approved