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

1,2

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).

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)

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 *)

Prog

(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

Crossrefs

Cf. A174120.

Sequence in context: A009845 A014342 A086274 * A128563 A227085 A192978

Adjacent sequences: A174118 A174119 A174120 * A174122 A174123 A174124

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Mar 08 2010

Status

approved