A124011 Add three, add six, add nine, ....

5, 8, 14, 23, 35, 50, 68, 89, 113, 140, 170, 203, 239, 278, 320, 365, 413, 464, 518, 575, 635, 698, 764, 833, 905, 980, 1058, 1139, 1223, 1310, 1400, 1493, 1589, 1688, 1790, 1895, 2003, 2114, 2228, 2345, 2465, 2588, 2714, 2843, 2975, 3110, 3248, 3389, 3533, 3680

Offset

1,1

Comments

Found on a quiz.

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) = 3*n*(n-1)/2 + 5 = 3*A000217(n-1) + 5 = A045943(n) + 5.

a(n) = 3*n + a(n-1) - 3 with a(1)=5. - Vincenzo Librandi, Nov 28 2009

G.f.: x*(5 - 7*x + 5*x^2)/(1-x)^3. - Colin Barker, Jan 14 2012

3*(8*a(n) - 37) = A016945(n-1)^2. - Vincenzo Librandi, Feb 15 2012

From Elmo R. Oliveira, Feb 11 2025: (Start)

E.g.f.: exp(x)*(5 + 3*x^2/2) - 5.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {5, 8, 14}, 50] (* Vincenzo Librandi, Feb 15 2012 *)
Table[(3x^2-3x+10)/2, {x, 50}] (* Harvey P. Dale, Jul 25 2019 *)
Accumulate[3*Range[0, 50]]+5 (* Harvey P. Dale, Jan 16 2024 *)

Prog

(Magma) I:=[5, 8, 14]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 15 2012
(PARI) a(n)=3*n*(n-1)/2+5 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217, A016945, A045943.

Sequence in context: A314526 A092590 A065394 * A101835 A192522 A133641

Adjacent sequences: A124008 A124009 A124010 * A124012 A124013 A124014

Keyword

nonn,easy

Author

Ruben Fritzon (ruben.fritzon(AT)edu.ovanaker.se), Dec 11 2006

Extensions

More terms from Graham Roy (groy(AT)ashland.edu), Dec 14 2006

Additional comments from Christopher N. Swanson (cswanson(AT)ashland.edu), R. J. Mathar, Dec 14 2006

Status

approved