cp's OEIS Frontend

A152745 5 times hexagonal numbers: 5*n*(2*n-1).

%I A152745 #34 Sep 08 2022 08:45:39
%S A152745 0,5,30,75,140,225,330,455,600,765,950,1155,1380,1625,1890,2175,2480,
%T A152745 2805,3150,3515,3900,4305,4730,5175,5640,6125,6630,7155,7700,8265,
%U A152745 8850,9455,10080,10725,11390,12075,12780,13505,14250,15015
%N A152745 5 times hexagonal numbers: 5*n*(2*n-1).
%C A152745 Sequence found by reading the line from 0, in the direction 0, 5, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - _Omar E. Pol_, Sep 18 2011
%C A152745 Also sequence found by reading the line from 0, in the direction 0, 5, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is one of the four semi-diagonals of the spiral. - _Omar E. Pol_, Oct 14 2011
%H A152745 Ivan Panchenko, <a href="/A152745/b152745.txt">Table of n, a(n) for n = 0..1000</a>
%H A152745 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A152745 a(n) = 10*n^2 - 5*n = A000384(n)*5.
%F A152745 a(n) = a(n-1) + 20*n-15 (with a(0)=0). - _Vincenzo Librandi_, Nov 26 2010
%F A152745 From _G. C. Greubel_, Sep 01 2018: (Start)
%F A152745 G.f.: 5*x*(1+ 3*x)/(1-x)^3.
%F A152745 E.g.f.: 5*x*(1+2*x)*exp(x). (End)
%F A152745 From _Vaclav Kotesovec_, Sep 02 2018: (Start)
%F A152745 Sum_{n>=1} 1/a(n) = 2*log(2)/5.
%F A152745 Sum_{n>=1} (-1)^n/a(n) = log(2)/5 - Pi/10. (End)
%t A152745 LinearRecurrence[{3,-3,1}, {0, 5, 30}, 50] (* or *) Table[5*n*(2*n-1), {n,0,50}] (* _G. C. Greubel_, Sep 01 2018 *)
%o A152745 (PARI) a(n)=5*n*(2*n-1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A152745 (Magma) [5*n*(2*n-1): n in [0..50]]; // _G. C. Greubel_, Sep 01 2018
%Y A152745 Cf. A000384, A085250, A152746.
%Y A152745 Bisection of A028895.
%K A152745 easy,nonn
%O A152745 0,2
%A A152745 _Omar E. Pol_, Dec 12 2008