OFFSET
0,2
COMMENTS
This is the triangular equivalent of A008574 (square units forming perimeter of a square).
The height of each triangle is n+1 units.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Michel Marcus, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(0)=1 and a(1)=4; thereafter a(n) = (n+1)^2-(n-2)^2 = 6*n-3.
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
a(n) = A016945(n-1), n>1.
MATHEMATICA
CoefficientList[Series[(1 + x) (1 + x + x^2)/(1 - x)^2, {x, 0, 53}], x] (* Michael De Vlieger, Mar 21 2016 *)
PROG
(PARI) a(n)=if(n<2, 3*n+1, 6*n-3) \\ Charles R Greathouse IV, Mar 19 2016
(PARI) Vec((1+x)*(1+x+x^2)/(1-x)^2 + O(x^50)) \\ Colin Barker, Mar 20 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter M. Chema, Mar 18 2016
STATUS
approved