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 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 (list; graph; refs; listen; history; text; internal format)
 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 17-gonal numbers. Sum of the numbers from 7n to 8n. - Wesley Ivan Hurt, Dec 23 2015 Also the number of 4-cycles 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/(1-x)^3. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) 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 (3-cycles in the triangular honeycomb obtuse knight graph), A290391 (5-cycles), A290392 (6-cycles). - 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

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Last modified December 12 17:59 EST 2019. Contains 329960 sequences. (Running on oeis4.)