OFFSET
0,2
COMMENTS
Row sums of number triangle A113128. - Paul Barry, Oct 14 2005
The Engel expansion of 1 + exp(1/8)*sqrt(2*Pi)*erf(1/(2*sqrt(2)))/5 = 1.2175306077808... - Benedict W. J. Irwin, Dec 16 2016
LINKS
Leo Tavares, Square illustration
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(0) = 1, a(1) = 5, a(2) = 12; then a(n+1) = a(n) + 8, n > 2.
From Paul Barry, Oct 14 2005: (Start)
G.f.: (1+x)^3/(1-x)^2;
a(n) = 8n - 4 + 4*C(0, n) + C(1, n);
a(n) = C(n+1, n) + 3*C(n, n-1) + 3*C(n-1, n-2) + C(n-2, n-3). (End)
a(n) = A017113(n-1), n > 1. - R. J. Mathar, Sep 12 2008
EXAMPLE
a(6) = 44 = 8 + a(5) = 8 + 36.
MATHEMATICA
CoefficientList[Series[(z^3 + 3*z^2 + 3*z + 1)/(z - 1)^2, {z, 0, 100}], z] (* and *) Join[{1, 5}, Table[4*(2*(n + 1) + 1), {n, 0, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jul 17 2011 *)
PROG
(PARI) a(n)=if(n>1, 8*n-4, 4*n+1) \\ Charles R Greathouse IV, Dec 16 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jul 22 2003
STATUS
approved