OFFSET
0,2
COMMENTS
Partial sums of A030195. The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))g(x(1+x)).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,0,-3).
FORMULA
G.f.: 1/((1-x)(1-3x-3x^2));
a(n) = 4a(n-1) - 3a(n-3);
a(n) = Sum_{k=0..n} (Sum_{i=0..n} C(k, i-k))*3^k.
a(n) = 3(a(n-1) + a(n-2)) + 1, n > 1. [Gary Detlefs, Jun 21 2010]
MAPLE
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=3*a[n-1]+3*a[n-2]+1 od: seq(a[n], n=1..33); # Zerinvary Lajos, Dec 14 2008
MATHEMATICA
Join[{a=0, b=1}, Table[c=3*b+3*a+1; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{4, 0, -3}, {1, 4, 16}, 40] (* Vincenzo Librandi, Aug 18 2017 *)
PROG
(Magma) I:=[1, 4, 16]; [n le 3 select I[n] else 4*Self(n-1)-3*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Aug 18 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 16 2005
STATUS
approved