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,....

3, 6, 12, 16, 24, 30, 42, 48, 60, 66, 78, 86, 102, 114, 138, 148, 168, 174, 186, 194, 210, 222, 246, 258, 282, 294, 318, 334, 366, 390, 438, 456, 492, 498, 510, 518, 534, 546, 570, 582, 606, 618, 642, 658, 690, 714, 762, 782, 822, 834, 858, 874, 906, 930, 978

Offset: 0

Author

Roger L. Bagula, Mar 27 2006

Keywords

• nonn

Comments

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.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000032, A084230.

Cf. A006046.

Programs

Maple

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);

Mathematica

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}]

Formula

a(n) = A006046(n+2) + A006046(n) for n>=1.

Extensions

Edited by N. J. A. Sloane, Apr 15 2006