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A124011 Add three, add six, add nine, .... 2
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
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 *)
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
Sequence in context: A314526 A092590 A065394 * A101835 A192522 A133641
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 March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)