A119587 2^n + 1 - 2*Fibonacci(n+1).

0, 1, 1, 3, 7, 17, 39, 87, 189, 403, 847, 1761, 3631, 7439, 15165, 30795, 62343, 125905, 253783, 510759, 1026685, 2061731, 4136991, 8295873, 16627167, 33311647, 66716029, 133582107, 267406999, 535206833, 1071049287

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (4,-4,-1,2).

Formula

a(n) = 2^n + 1 - 2*Fibonacci(n+1) = 2^n + 1 + Fibonacci(n) - Fibonacci(n+3) = 2^n + 1 - Fibonacci(n) - Lucas(n). a(n) = 2(2^(n-1) - Fibonacci(n+1)) + 1, for n > 0. a(n) = A000051(n) - A006355(n+2) = A000051(n) - A000045(n) - A000032(n). a(n) = A101220(2,2,n-1) - A101220(1,1,n-3), for n > 2. a(n) = A008466(n) - A000071(n-1), for n > 0. a(n) = 2*A008466(n-1) + 1, for n > 0.

a(n) = 2*A101220(2,2,n-2) + 1, for n > 1. a(n) = Sum[2^(n-k)Fibonacci(k) - Fibonacci(k-2),{k,0,n}] = antidiagonal sums of A118654. a(n+1) - a(n) = 2(2^(n-1) - Fibonacci(n)), for n > 0. a(n+1) - a(n) = 2*A027934(n-2), for n > 1. a(n+1) - a(n) = 2*A101220(1,2,n-1), for n > 0. a(0) = 0; a(1) = 1; a(n) = a(n-1) + a(n-2) + 2^(n-2) - 1, for n > 1. a(0) = 0; a(1) = 1; a(2) = 1; a(3) = 3; a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4), for n > 3.

O.g.f. = x(1-3x+3x^2)/((1-x)(1-2x)(1-x-x^2)).

Mathematica

Table[2^n + 1 - 2 Fibonacci[n + 1], {n, 0, 30}]

Crossrefs

Cf. A000032, A000045, A000051, A000071, A006355, A008466, A027934, A101220, A118654.

Sequence in context: A141199 A368655 A003478 * A127984 A157029 A191825

Adjacent sequences: A119584 A119585 A119586 * A119588 A119589 A119590

Keyword

nonn

Author

Ross La Haye, May 31 2006, Jun 27 2007

Status

approved