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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified July 22 06:22 EDT 2019. Contains 325213 sequences. (Running on oeis4.)