A048492 a(n) = ( 8*(2^n) - n^2 - 3*n - 6 )/2.

1, 3, 8, 20, 47, 105, 226, 474, 977, 1991, 4028, 8112, 16291, 32661, 65414, 130934, 261989, 524115, 1048384, 2096940, 4194071, 8388353, 16776938, 33554130, 67108537, 134217375, 268435076, 536870504, 1073741387, 2147483181

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Partial sums of A000325, starting at n=1. - Klaus Brockhaus, Oct 13 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Crossrefs

a(n)=T(0, n)+T(1, n-1)+...+T(n, 0), array T given by A048483.

Cf. A000325 (2^n - n), A145070. - Klaus Brockhaus, Oct 13 2008

Programs

ARIBAS

a:=0; for n:=1 to 30 do a:=a+2**n-n; write(a, ","); end; # Klaus Brockhaus, Oct 13 2008

Magma

[( 8*(2^n) -n^2 -3*n -6 )/2: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011

Mathematica

lst={};s=0;Do[s+=2^n-n;AppendTo[lst, s], {n, 5!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 30 2008 *)
Table[(8*2^n-n^2-3n-6)/2,{n,0,30}]
LinearRecurrence[{5,-9,7,-2},{1,3,8,20},40] (* Harvey P. Dale, Aug 28 2019 *)

PARI

Vec((2*x^2-2*x+1) / ((x-1)^3*(2*x-1)) + O(x^100)) \\ Colin Barker, Oct 27 2014

Formula

a(0) = 1; a(n) = a(n-1) + 2^(n+1) - (n+1) for n > 0. - Klaus Brockhaus, Oct 13 2008

From Colin Barker, Oct 27 2014: (Start)

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

a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4).

G.f.: (2*x^2-2*x+1) / ((x-1)^3*(2*x-1)).

(End)

Extensions

Better description from Frank Ellermann, Mar 16 2002

Corrected by T. D. Noe, Nov 08 2006