A179744 a(0) = 1, a(n) = 3*2^(n-1) - n for n>0.

1, 2, 4, 9, 20, 43, 90, 185, 376, 759, 1526, 3061, 6132, 12275, 24562, 49137, 98288, 196591, 393198, 786413, 1572844, 3145707, 6291434, 12582889, 25165800, 50331623, 100663270, 201326565, 402653156, 805306339, 1610612706, 3221225441

Offset

0,2

Comments

Equals row sums of triangle A179743.

Essentially the same as A133095 and A123720. - R. J. Mathar, Jul 26 2010

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(0) = 1, a(1) = 2; a(n) = 2*a(n-1) + (n-2) for n>1.

G.f. 1-x*(2-4*x+3*x^2) / ( (2*x-1)*(x-1)^2 ). - R. J. Mathar, May 03 2013

Example

a(5) = 43 = 2*a(4) + 3 = 2*20 + 3
a(5) = 43 = sum of row 5 terms, triangle A179743: (1 + 5 + 8 + 12 + 16 + 1).

Mathematica

a[0] = 1; a[1] = 2; a[n_] := a[n] = 2 a[n - 1] + (n - 2); Array[a, 35, 0] (* Robert G. Wilson v, Aug 03 2010 *)

Prog

(PARI) a(n)=3*2^n\2-n \\ Charles R Greathouse IV, May 03 2013

Crossrefs

Cf. A179743.

Sequence in context: A350092 A175104 A123720 * A266930 A034007 A109975

Adjacent sequences: A179741 A179742 A179743 * A179745 A179746 A179747

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 25 2010

Extensions

More terms from Robert G. Wilson v, Aug 03 2010

Status

approved