A174121 Partial sums of A001580.

1, 4, 12, 29, 61, 118, 218, 395, 715, 1308, 2432, 4601, 8841, 17202, 33782, 66775, 132567, 263928, 526396, 1051045, 2100021, 4197614, 8392402, 16781539, 33559331, 67114388, 134223928, 268442385, 536878625, 1073750378, 2147493102, 4294977711, 8589946031

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 08 2010

Keywords

• nonn
• easy

Comments

A001580 2^n+n^2 -> 1,3,8,17,32,57,100,177,320,593,1124,..

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

Crossrefs

Cf. A174120.

Programs

Mathematica

f[n_]:=Sum[2^i+i^2,{i,0,n}];Table[f[n],{n,0,5!}]
Accumulate[Table[2^n+n^2,{n,0,50}]] (* or *) LinearRecurrence[{6,-14,16,-9,2},{1,4,12,29,61},50] (* Harvey P. Dale, Sep 23 2019 *)

PARI

Vec(x*(1-2*x+2*x^2-3*x^3)/((1-x)^4*(1-2*x)) + O(x^40)) \\ Colin Barker, Feb 26 2016

Formula

From Colin Barker, Feb 26 2016: (Start)

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

a(n) = 6*a(n-1)-14*a(n-2)+16*a(n-3)-9*a(n-4)+2*a(n-5) for n>5.

G.f.: x*(1-2*x+2*x^2-3*x^3) / ((1-x)^4*(1-2*x)).

(End)