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A152741 13 times triangular numbers. 5
0, 13, 39, 78, 130, 195, 273, 364, 468, 585, 715, 858, 1014, 1183, 1365, 1560, 1768, 1989, 2223, 2470, 2730, 3003, 3289, 3588, 3900, 4225, 4563, 4914, 5278, 5655, 6045, 6448, 6864, 7293, 7735, 8190, 8658, 9139, 9633, 10140, 10660, 11193, 11739, 12298, 12870 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 13,... and the same line from 0, in the direction 0, 39,..., in the square spiral whose vertices are the generalized 15-gonal numbers. - Omar E. Pol, Oct 03 2011
Sum of the numbers from 6n to 7n. - Wesley Ivan Hurt, Dec 22 2015
LINKS
FORMULA
a(n) = 13*n*(n+1)/2 = 13 * A000217(n).
a(n) = a(n-1)+13*n (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
a(n) = A069126(n+1) - 1. - Omar E. Pol, Oct 03 2011
From Wesley Ivan Hurt, Dec 22 2015: (Start)
G.f.: 13*x/(1-x)^3.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.
a(n) = Sum_{i=6n..7n} i. (End)
E.g.f.: 13*x*(2+x)*exp(x)/2. - G. C. Greubel, Sep 01 2018
From Amiram Eldar, Feb 21 2023: (Start)
Sum_{n>=1} 1/a(n) = 2/13.
Sum_{n>=1} (-1)^(n+1)/a(n) = (4*log(2) - 2)/13.
Product_{n>=1} (1 - 1/a(n)) = -(13/(2*Pi))*cos(sqrt(21/13)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (13/(2*Pi))*cos(sqrt(5/13)*Pi/2). (End)
MAPLE
A152741:=n->13*n*(n+1)/2: seq(A152741(n), n=0..60); # Wesley Ivan Hurt, Dec 22 2015
MATHEMATICA
Table[13*n*(n-1)/2, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
CoefficientList[Series[13 x/(1 - x)^3, {x, 0, 50}], x] (* Wesley Ivan Hurt, Dec 22 2015 *)
PROG
(Magma) [13*n*(n+1)/2 : n in [0..60]]; // Wesley Ivan Hurt, Dec 22 2015
(PARI) a(n)=13*n*(n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Sequence in context: A299055 A158647 A283123 * A168235 A258597 A299816
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 12 2008
STATUS
approved

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)