A017642 a(n) = (12*n+10)^2.

100, 484, 1156, 2116, 3364, 4900, 6724, 8836, 11236, 13924, 16900, 20164, 23716, 27556, 31684, 36100, 40804, 45796, 51076, 56644, 62500, 68644, 75076, 81796, 88804, 96100, 103684, 111556, 119716

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Formula

From Wesley Ivan Hurt, Dec 22 2020: (Start)

G.f.: 4*(25 + 46*x + x^2)/(1 - x)^3.

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

a(n) = 144*n^2 + 240*n + 100.

a(n) = A017641(n)^2. (End)

Example

a(5) = (12*5+10)^2 = 70^2 = 4900.

Mathematica

(12*Range[0, 30]+10)^2 (* or *) LinearRecurrence[{3, -3, 1}, {100, 484, 1156}, 30] (* Harvey P. Dale, May 08 2017 *)
CoefficientList[Series[4*(25 + 46 x + x^2)/(1 - x)^3, {x, 0, 40}], x] (* Wesley Ivan Hurt, Dec 22 2020 *)

Prog

(PARI) a(n)=(12*n+10)^2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [(12*n+10)^2 : n in [0..40]]; // Wesley Ivan Hurt, Dec 22 2020

Crossrefs

Cf. A016969, A016970, A017641, A017643.

Sequence in context: A334707 A017510 A290654 * A093004 A003588 A115695

Adjacent sequences: A017639 A017640 A017641 * A017643 A017644 A017645

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved