A174339 a(n) = 109*n^2.

0, 109, 436, 981, 1744, 2725, 3924, 5341, 6976, 8829, 10900, 13189, 15696, 18421, 21364, 24525, 27904, 31501, 35316, 39349, 43600, 48069, 52756, 57661, 62784, 68125, 73684, 79461, 85456, 91669, 98100, 104749, 111616, 118701, 126004, 133525

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

From Vincenzo Librandi, Feb 25 2012: (Start)

G.f.: 109*x*(1+x)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

a(n) = (55n)^2 - (54n)^2 = (10n)^2 + (3n)^2. (End) [G.f. corrected by Georg Fischer, May 11 2019]

Mathematica

CoefficientList[Series[109*x*(x+1)/(1-x)^3, {x, 0, 33}], x]
109*Range[0, 40]^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 109, 436}, 40] (* Harvey P. Dale, May 18 2012 *)

Prog

(Magma) [109*n^2: n in [0..50]]; /* or */ I:=[0, 109, 436]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 25 2012
(PARI) a(n)=109*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A139644 A360490 A270249 * A142640 A126856 A142915

Adjacent sequences: A174336 A174337 A174338 * A174340 A174341 A174342

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 16 2010

Status

approved