OFFSET
0,2
COMMENTS
Row sums of A106513.
Equals eigensequence of a triangle with the Pell series as the left border and the rest 1's. - Gary W. Adamson, Jul 24 2010
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-3,-2).
FORMULA
a(n) = Sum_{k=0..n} 2^(n-k-1)*((1-sqrt(2))^k + (1+sqrt(2))^k).
a(n) = Sum_{k=0..n} Sum_{j=0..floor((n+1)/2)} binomial(n+1, 2*j+k+1)*2^j.
a(n) = Pell(n+3) - Pell(n+2) - 2^(n+1) = A001333(n+2) - 2^(n+1). - Ralf Stephan, Jun 02 2007
From G. C. Greubel, Aug 05 2021: (Start)
Sum_{j=0..n} a(j) = A094706(n+1). (End)
MATHEMATICA
Table[(LucasL[n+2, 2] - 2^(n+2))/2, {n, 0, 40}] (* G. C. Greubel, Aug 05 2021 *)
PROG
(Magma) I:=[1, 3, 9]; [n le 3 select I[n] else 4*Self(n-1) -3*Self(n-2) -2*Self(n-3): n in [1..41]]; // G. C. Greubel, Aug 05 2021
(Sage) [(lucas_number2(n+2, 2, -1) - 2^(n+2))/2 for n in (0..40)] # G. C. Greubel, Aug 05 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 05 2005
STATUS
approved