login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A174121 Partial sums of A001580. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)