A193912 Partial sums of A193911.

1, 4, 11, 25, 50, 93, 162, 272, 439, 694, 1069, 1627, 2432, 3611, 5292, 7730, 11181, 16156, 23167, 33237, 47390, 67673, 96134, 136868, 193971, 275634, 390049, 553599, 782668, 1110023, 1568432, 2223430, 3140553, 4450872, 6285459, 8906457, 12576010, 17818405

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,-8,7,3,-6,2).

Formula

a(n) = Sum_{i=1..n} 1/8*(2^(i/2+2)*((10-7*sqrt(2))*(-1)^(i) + 10 + 7*sqrt(2))-(-1)^(i)-2*i*(i+12)-79).

G.f.: x*(1+x-x^2)/((1-x)^4*(1+x)*(1-2*x^2)). - Alexander R. Povolotsky, Aug 12 2011

a(n) = (1/32)*( (-1/2)^n + 32*(41*sqrt(2)-58)*(sqrt(2)-2)^n - 32*(58+41*sqrt(2))*(-2-sqrt(2))^n ).

Example

We have A193911(1)=1, A193911(2)=3, and A193911(3)=7. Thus a(1)=1, a(2)=4, and a(3)=11.

Mathematica

LinearRecurrence[{3, 0, -8, 7, 3, -6, 2}, {1, 4, 11, 25, 50, 93, 162}, 40] (* Harvey P. Dale, Sep 09 2015 *)
CoefficientList[Series[(1 + x - x^2)/((1 - x)^4*(1 + x)*(1 - 2*x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 25 2017 *)

Prog

(PARI) my(x='x+O('x^50)); Vec((1+x-x^2)/((1-x)^4*(1+x)*(1-2*x^2))) \\ G. C. Greubel, Feb 25 2017

Crossrefs

Sequence in context: A036837 A215052 A011851 * A136395 A014160 A014162

Adjacent sequences: A193909 A193910 A193911 * A193913 A193914 A193915

Keyword

nonn,easy

Author

Jeffrey R. Goodwin, Aug 08 2011

Status

approved