A145070 Partial sums of A006127, starting at n=1.

3, 9, 20, 40, 77, 147, 282, 546, 1067, 2101, 4160, 8268, 16473, 32871, 65654, 131206, 262295, 524457, 1048764, 2097360, 4194533, 8388859, 16777490, 33554730, 67109187, 134218077, 268435832, 536871316, 1073742257, 2147484111

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Formula

a(1) = 3; a(n) = a(n-1) + 2^n + n for n > 1.

From Colin Barker, Oct 27 2014: (Start)

a(n) = (-4+2^(2+n)+n+n^2)/2.

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

G.f.: x*(2*x^2-6*x+3) / ((x-1)^3*(2*x-1)).

(End)

Example

a(2) = a(1) + 2^2 + 2 = 3 + 4 + 2 = 9; a(3) = a(2) + 2^3 + 3 = 9 + 8 + 3 = 20.

Maple

A145070:=n->(-4+2^(2+n)+n+n^2)/2: seq(A145070(n), n=1..50); # Wesley Ivan Hurt, Jan 22 2017

Mathematica

lst={}; s=0; Do[s+=2^n+n; AppendTo[lst, s], {n, 5!}]; lst
Accumulate[Table[2^n+n, {n, 50}]] (* or *) LinearRecurrence[{5, -9, 7, -2}, {3, 9, 20, 40}, 50] (* Harvey P. Dale, Aug 22 2020 *)

Prog

(ARIBAS) a:=0; for n:=1 to 30 do a:=a+2**n+n; write(a, ", "); end;
(PARI) Vec(x*(2*x^2-6*x+3) / ((x-1)^3*(2*x-1)) + O(x^100)) \\ Colin Barker, Oct 27 2014

Crossrefs

Cf. A006127 (2^n + n), A000325 (2^n - n), A048492 (partial sums of A000325, starting at n=1).

Sequence in context: A202349 A192951 A027114 * A011796 A164680 A210634

Adjacent sequences: A145067 A145068 A145069 * A145071 A145072 A145073

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Sep 30 2008

Extensions

Edited by Klaus Brockhaus, Oct 14 2008

Status

approved