

A194715


15 times triangular numbers.


6



0, 15, 45, 90, 150, 225, 315, 420, 540, 675, 825, 990, 1170, 1365, 1575, 1800, 2040, 2295, 2565, 2850, 3150, 3465, 3795, 4140, 4500, 4875, 5265, 5670, 6090, 6525, 6975, 7440, 7920, 8415, 8925, 9450, 9990, 10545, 11115, 11700, 12300, 12915, 13545, 14190, 14850, 15525
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OFFSET

0,2


COMMENTS

Sequence found by reading the line from 0, in the direction 0, 15, ... and the same line from 0, in the direction 0, 45, ..., in the square spiral whose vertices are the generalized 17gonal numbers.
Sum of the numbers from 7n to 8n.  Wesley Ivan Hurt, Dec 23 2015
Also the number of 4cycles in the (n+6)triangular honeycomb obtuse knight graph.  Eric W. Weisstein, Jul 28 2017


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Eric Weisstein's World of Mathematics, Graph Cycle
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 15*n*(n+1)/2 = 15*A000217(n) = 5*A045943(n) = 3*A028895(n) = A069128(n+1)  1.
From Wesley Ivan Hurt, Dec 23 2015: (Start)
G.f.: 15*x/(1x)^3.
a(n) = 3*a(n1)3*a(n2)+a(n3) for n>2.
a(n) = Sum_{i=7n..8n} i. (End)


MAPLE

A194715:=n>15*n*(n+1)/2: seq(A194715(n), n=0..60); # Wesley Ivan Hurt, Dec 23 2015


MATHEMATICA

15*Accumulate[Range[0, 60]] (* Harvey P. Dale, Feb 12 2012 *)
Table[15 n (n + 1)/2, {n, 0, 60}] (* Wesley Ivan Hurt, Dec 23 2015 *)
15 Binomial[Range[20], 2] (* Eric W. Weisstein, Jul 28 2017 *)
15 PolygonalNumber[Range[0, 20]] (* Eric W. Weisstein, Jul 28 2017 *)


PROG

(MAGMA) [15*n*(n+1)/2: n in [0..50]]; // Vincenzo Librandi, Oct 04 2011
(PARI) a(n)=15*n*(n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A000217, A028895, A035008, A045943, A069128, A163756.
Cf. A001105 (3cycles in the triangular honeycomb obtuse knight graph), A290391 (5cycles), A290392 (6cycles).  Eric W. Weisstein, Jul 29 2017
Sequence in context: A066763 A164788 A033849 * A060536 A014634 A303857
Adjacent sequences: A194712 A194713 A194714 * A194716 A194717 A194718


KEYWORD

nonn,easy


AUTHOR

Omar E. Pol, Oct 03 2011


STATUS

approved



