cp's OEIS Frontend

A116593 a(n) = b(n+2) + b(n), where b(n) = A006046(n) is the sequence defined by b(0)=0, b(1)=1, b(n) = 2*b((n-1)/2) + b((n+1)/2) for n =3,5,7,... and b(n) = 3*b(n/2) for n =2,4,6,....

%I A116593 #12 Dec 13 2017 02:45:11
%S A116593 3,6,12,16,24,30,42,48,60,66,78,86,102,114,138,148,168,174,186,194,
%T A116593 210,222,246,258,282,294,318,334,366,390,438,456,492,498,510,518,534,
%U A116593 546,570,582,606,618,642,658,690,714,762,782,822,834,858,874,906,930,978
%N A116593 a(n) = b(n+2) + b(n), where b(n) = A006046(n) is the sequence defined by b(0)=0, b(1)=1, b(n) = 2*b((n-1)/2) + b((n+1)/2) for n =3,5,7,... and b(n) = 3*b(n/2) for n =2,4,6,....
%C A116593 A similar definition applied to the Fibonacci sequence (A000045) leads to the Lucas sequence (A000032). b(n) in the definition is also the number of odd entries in the first n rows of the Pascal triangle.
%H A116593 G. C. Greubel, <a href="/A116593/b116593.txt">Table of n, a(n) for n = 0..5000</a>
%F A116593 a(n) = A006046(n+2) + A006046(n) for n>=1.
%p A116593 b:=proc(n) option remember: if n = 0 then 0 elif n=1 then 1 elif n mod 2 = 0 then 3*b(n/2) else 2*b((n-1)/2)+b((n+1)/2) fi end: a:=n->b(n+2)+b(n): seq(a(n),n=0..60);
%t A116593 b[0] := 0 b[1] := 1; b[n_?EvenQ] := b[n] = 3*b[n/2]; b[n_?OddQ] := b[n] = 2*b[(n - 1)/2] + b[(n + 1)/2]; L[0] = 1; L[n_] := L[n] = b[n - 1] + b[n + 1]; Table[L[n], {n, 1, 200}]
%Y A116593 Cf. A000032, A084230.
%Y A116593 Cf. A006046.
%K A116593 nonn
%O A116593 0,1
%A A116593 _Roger L. Bagula_, Mar 27 2006
%E A116593 Edited by _N. J. A. Sloane_, Apr 15 2006