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A124011 Add three, add six, add nine, .... 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Found on a quiz.

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

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

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 *)

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

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

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Last modified September 21 15:09 EDT 2019. Contains 327270 sequences. (Running on oeis4.)