A097067 Expansion of g.f. (1-4*x+5*x^2)/(1-2*x)^2.

1, 0, 1, 4, 12, 32, 80, 192, 448, 1024, 2304, 5120, 11264, 24576, 53248, 114688, 245760, 524288, 1114112, 2359296, 4980736, 10485760, 22020096, 46137344, 96468992, 201326592, 419430400, 872415232, 1811939328, 3758096384, 7784628224, 16106127360, 33285996544, 68719476736

Offset: 0

Author

Paul Barry, Jul 22 2004

Keywords

• nonn
• easy

Comments

Binomial transform of A097065. Binomial transform is (n-2)*2^(n-1)+2, or A048495 with an extra leading 1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

Essentially the same as A001787.

Cf. A048495, A097065.

Programs

Magma

[(n-1)*2^(n-2)+5*0^n/4 : n in [0..30]]; // Vincenzo Librandi, Sep 25 2011

Maple

a:=n->abs(floor(sum (2^(n-1),j=1..n))): seq(a(n),n=-1..28); # Zerinvary Lajos, Jun 27 2007

PARI

Vec((1-4*x+5*x^2)/(1-2*x)^2 + O(x^50)) \\ Altug Alkan, Nov 13 2015

Formula

a(n) = (n-1)*2^(n-2) + 5*0^n/4.

a(n) = 4*a(n-1) - 4*a(n-2), n > 1.

a(n+1) = A001787(n).

E.g.f.: (5 - exp(2*x)*(1 - 2*x))/4. - Stefano Spezia, Jul 01 2023