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A067728 a(n) = 2*n^2 + 8*n. 18
10, 24, 42, 64, 90, 120, 154, 192, 234, 280, 330, 384, 442, 504, 570, 640, 714, 792, 874, 960, 1050, 1144, 1242, 1344, 1450, 1560, 1674, 1792, 1914, 2040, 2170, 2304, 2442, 2584, 2730, 2880, 3034, 3192, 3354, 3520, 3690, 3864, 4042, 4224, 4410, 4600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Positive numbers k such that 8*(8 + k) is a perfect square.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n+1) = 2*n*n + 12*n + 10. - Frank Ellermann

a(n) = Sum_{k=0..n} Sum_{j=4..n} (j - k), n >= 4. - Zerinvary Lajos, May 11 2007

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jul 08 2012

G.f.: 2*x*(5-3*x)/(1-x)^3. - Vincenzo Librandi, Jul 08 2012

MAPLE

a:=n->sum(sum(j-k, j=4..n), k=0..n): seq(a(n), n=4..49); # Zerinvary Lajos, May 11 2007

MATHEMATICA

Select[ Range[10000], IntegerQ[ Sqrt[ 8(8 + # )]] & ]

CoefficientList[Series[2*(5-3*x)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *)

PROG

(PARI) a(n)=2*n*(n+4) \\ Charles R Greathouse IV, Dec 07 2011

(MAGMA) [2*n*(n+4): n in [1..50]] // Vincenzo Librandi, Jul 08 2012

CROSSREFS

Cf. 7: A067727, 6: A067726, 5: A067724, 3: A067725.

Cf. A000217, A005563, A140091, A140681, A212331.

Sequence in context: A267431 A162817 A103573 * A058504 A250798 A250576

Adjacent sequences:  A067725 A067726 A067727 * A067729 A067730 A067731

KEYWORD

nonn,easy

AUTHOR

Robert G. Wilson v, Feb 05 2002

STATUS

approved

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Last modified November 21 15:03 EST 2018. Contains 317449 sequences. (Running on oeis4.)