login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195319 Three times second hexagonal numbers: 3*n*(2*n+1). 5
0, 9, 30, 63, 108, 165, 234, 315, 408, 513, 630, 759, 900, 1053, 1218, 1395, 1584, 1785, 1998, 2223, 2460, 2709, 2970, 3243, 3528, 3825, 4134, 4455, 4788, 5133, 5490, 5859, 6240, 6633, 7038, 7455, 7884, 8325, 8778, 9243, 9720, 10209, 10710, 11223 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 9, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Semi-axis opposite to A094159 in the same spiral.
Sum of the numbers from 2*n to 4*n. - Wesley Ivan Hurt, Nov 27 2015
From Peter M. Chema, Jan 21 2017: (Start)
Also 0 together with the partial sums of A017629.
Digit root is 0 together with period 3: repeat [9,3,9].
Final digits cycle a length period 10: repeat [0,9,0,3,8,5,4,5,8,3]. (End)
Sequence found by reading the line from 0, in the direction 0, 9, ..., in the triangle spiral. - Hans G. Oberlack, Dec 08 2018
LINKS
Hans G. Oberlack, Triangle spiral.
FORMULA
a(n) = 6*n^2 + 3*n = 3*A014105(n).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - Harvey P. Dale, Oct 13 2013
G.f.: 3*x*(3+x) / (1-x)^3. - Wesley Ivan Hurt, Nov 27 2015
a(n) = A000217(3*n) + 3*A000217(n). - Bruno Berselli, Aug 31 2017
E.g.f.: 3*x*(2*x+3)*exp(x). - G. C. Greubel, Dec 07 2018
From Amiram Eldar, Feb 27 2022: (Start)
Sum_{n>=1} 1/a(n) = 2*(1 - log(2))/3.
Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi/2 + log(2) - 2)/3. (End)
MAPLE
A195319:=n->6*n^2 + 3*n: seq(A195319(n), n=0..50); # Wesley Ivan Hurt, Nov 27 2015
MATHEMATICA
Table[6n^2+3n, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 9, 30}, 50] (* Harvey P. Dale, Oct 13 2013 *)
CoefficientList[Series[3 x (3 + x)/(1 - x)^3, {x, 0, 50}], x] (* Wesley Ivan Hurt, Nov 27 2015 *)
PROG
(Magma) [3*n*(2*n+1): n in [0..50]]; // Vincenzo Librandi, Sep 20 2011
(PARI) a(n)=3*n*(2*n+1) \\ Charles R Greathouse IV, Oct 16 2015
(Sage) [3*n*(2*n+1) for n in range(50)] # G. C. Greubel, Dec 07 2018
(GAP) List([0..30], n -> 3*n*(2*n+1)); # G. C. Greubel, Dec 07 2018
CROSSREFS
Bisection of A045943.
Sequence in context: A063150 A063161 A295867 * A073399 A225275 A005919
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 17 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 12:20 EST 2024. Contains 370255 sequences. (Running on oeis4.)