OFFSET
0,2
COMMENTS
Self-convolution of A122553.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(0)=1, a(n) = 9*n - 3 = A008591(n) - 3 for n > 0.
a(n) = 2*a(n-1) - a(n-2) for n > 2; a(0)=1, a(1)=6, a(2)=15.
a(n) = a(n-1) + 9 for n > 1; a(0)=1, a(1)=6.
G.f.: ((1 + 2*x)/(1 - x))^2.
Equals binomial transform of [1, 5, 4, -4, 4, -4, 4, ...]. - Gary W. Adamson, Dec 10 2007
a(n) = A017233(n-1) for n > 0. - Georg Fischer, Oct 21 2018
E.g.f.: exp(x)*(9*x - 3) + 4. - Stefano Spezia, Mar 07 2023
MAPLE
seq(coeff(series(((1+2*x)/(1-x))^2, x, n+1), x, n), n = 0 .. 60); # Muniru A Asiru, Oct 21 2018
MATHEMATICA
Join[{1}, LinearRecurrence[{2, -1}, {6, 15}, 60]] (* Harvey P. Dale, Jun 12 2012 *)
PROG
(PARI) a(n)=max(9*n-3, 1) \\ Charles R Greathouse IV, Jan 17 2012
(PARI) Vec((1 + 2*x)^2 / (1 - x)^2 + O(x^100)) \\ Colin Barker, Jan 22 2018
(GAP) a:=[6, 15];; for n in [3..60] do a[n]:=2*a[n-1]-a[n-2]; od; Concatenation([1], a); # Muniru A Asiru, Oct 21 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Sep 23 2006
EXTENSIONS
Edited by N. J. A. Sloane, Jan 23 2018
STATUS
approved