OFFSET
0,2
COMMENTS
n-th difference of a(n), a(n-1), ..., a(0) is (6, 7, 8, ...).
More generally the main diagonal of the array defined by T(0,j) = j+1 with j>=0, T(i,0) = i+1 with i>=0, T(i,j) = T(i-1,j-1) + T(i-1,j) + A, is given by T(n,n) = 2^(n-1)*(n+2*A+2)-A. - Benoit Cloitre, Jun 17 2003
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Index entries for linear recurrences with constant coefficients, signature (5,-8,4).
FORMULA
From Benoit Cloitre, Jun 17 2003: (Start)
Main diagonal of the array defined by T(0, j) = j+1 with j>=0, T(i, 0) = i+1 with i>=0, T(i,j) = T(i-1,j-1)+T(i-1,j)+ 4. Therefore, for i = j = n:
a(n) = 2^(n-1)*(n+10)-4. (End)
a(0)=1, a(1)=7, a(2)=20; for n>2, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - Vincenzo Librandi, Sep 28 2011
a(n) = 2^(n-1)*(n+10)-4. G.f.: (1+2*x-7*x^2) / ((1-x)*(1-2*x)^2). - Colin Barker, Feb 18 2016
PROG
(Magma) [2^(n-1)*(n+10)-4: n in [0..30]]; // Vincenzo Librandi, Sep 28 2011
(PARI) Vec((1+2*x-7*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved