cp's OEIS Frontend

A270545 Number of equilateral triangle units forming perimeter of equilateral triangle.

%I A270545 #43 Mar 31 2016 03:54:41
%S A270545 1,4,9,15,21,27,33,39,45,51,57,63,69,75,81,87,93,99,105,111,117,123,
%T A270545 129,135,141,147,153,159,165,171,177,183,189,195,201,207,213,219,225,
%U A270545 231,237,243,249,255,261,267,273,279,285,291,297,303,309,315
%N A270545 Number of equilateral triangle units forming perimeter of equilateral triangle.
%C A270545 This is the triangular equivalent of A008574 (square units forming perimeter of a square).
%C A270545 The height of each triangle is n+1 units.
%H A270545 Colin Barker, <a href="/A270545/b270545.txt">Table of n, a(n) for n = 0..1000</a>
%H A270545 Michel Marcus, <a href="/A270545/a270545_2.jpg">Illustration of initial terms</a>
%H A270545 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A270545 a(0)=1 and a(1)=4; thereafter a(n) = (n+1)^2-(n-2)^2 = 6*n-3.
%F A270545 a(n) = 2*a(n-1)-a(n-2) for n>3. G.f.: (1+x)*(1+x+x^2) / (1-x)^2. - _Colin Barker_, Mar 20 2016
%F A270545 a(n) = A016945(n-1), n>1.
%t A270545 CoefficientList[Series[(1 + x) (1 + x + x^2)/(1 - x)^2, {x, 0, 53}], x] (* _Michael De Vlieger_, Mar 21 2016 *)
%o A270545 (PARI) a(n)=if(n<2,3*n+1,6*n-3) \\ _Charles R Greathouse IV_, Mar 19 2016
%o A270545 (PARI) Vec((1+x)*(1+x+x^2)/(1-x)^2 + O(x^50)) \\ _Colin Barker_, Mar 20 2016
%Y A270545 Cf. A016945, A008574.
%K A270545 nonn,easy
%O A270545 0,2
%A A270545 _Peter M. Chema_, Mar 18 2016