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A157716 One-eighth of triangular numbers (integers only). 2
0, 15, 17, 62, 66, 141, 147, 252, 260, 395, 405, 570, 582, 777, 791, 1016, 1032, 1287, 1305, 1590, 1610, 1925, 1947, 2292, 2316, 2691, 2717, 3122, 3150, 3585, 3615, 4080, 4112, 4607, 4641, 5166, 5202, 5757, 5795, 6380, 6420, 7035, 7077, 7722, 7766, 8441 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

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

FORMULA

G.f.: x^2*(15+2*x+15*x^2)/((1+x)^2*(1-x)^3 ). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]

a(n) =  (2*n-1 + 7/8*(-1)^n)^2 -1/64. - Robert Israel, Apr 20 2014

EXAMPLE

The first three members of A000217 that are divisible by 8 are A000217(0), A000217(15) and A000217(16), so a(1) = A000217(0)/8 = 0, a(2) = A000217(15)/8 = 15, a(3) = A000217(16)/8 = 17.

MAPLE

seq((2*n-1 + 7/8*(-1)^n)^2 - 1/64, n = 1 .. 1000); # Robert Israel, Apr 20 2014

MATHEMATICA

lst = {}; s = 0; Do[s += n/8; If[Floor[s] == s, AppendTo[lst, s]], {n, 0, 6!}]; lst

CROSSREFS

Cf. A000217, A101877.

Sequence in context: A002155 A290749 A091017 * A113968 A093812 A159840

Adjacent sequences:  A157713 A157714 A157715 * A157717 A157718 A157719

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Mar 04 2009

EXTENSIONS

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009

Definition edited by N. J. A. Sloane, Mar 08 2009

STATUS

approved

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Last modified March 26 20:47 EDT 2019. Contains 321535 sequences. (Running on oeis4.)