login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A213387 a(n) = 5*2^(n-1)-2-3*n. 2
0, 2, 9, 26, 63, 140, 297, 614, 1251, 2528, 5085, 10202, 20439, 40916, 81873, 163790, 327627, 655304, 1310661, 2621378, 5242815, 10485692, 20971449, 41942966, 83886003, 167772080, 335544237, 671088554, 1342177191 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Create an array m(i,j) as follows: m(1,j) =j*(j-1)/2 in the top row, m(i,1) =(i-1)^2 in the left column, and m(i,j)=m(i,j-1) + m(i-1,j) recursively in the main body, j>=1, i>=1. The sum of the terms in an antidiagonal is one term in this sequence, a(n) = sum_{k=1..n} m(n-k+1,k).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

FORMULA

a(n) = A095151(n-1) + 2*A000295(n-1) .

G.f. -x^2*(2+x) / (2*x-1)*(x-1)^2 ). - R. J. Mathar, Jun 29 2012

a(1)=0, a(2)=2, a(3)=9, a(n)=4*a(n-1)-5*a(n-2)+2*a(n-3). - Harvey P. Dale, Sep 28 2012

EXAMPLE

For n=5, m(5,1)=16, m(4,2)=15, m(3,3)=11, m(2,4)=11, m(1,5)=10 gives the sum 63=2*A000295(4)+A095151(4)=2*11+41

MATHEMATICA

Table[5*2^(n-1)-2-3n, {n, 30}] (* or *) LinearRecurrence[{4, -5, 2}, {0, 2, 9}, 30] (* Harvey P. Dale, Sep 28 2012 *)

CROSSREFS

Cf. A000295, A095151, A000217, A000290

Sequence in context: A221574 A082289 A014150 * A215184 A136429 A091469

Adjacent sequences: A213384 A213385 A213386 * A213388 A213389 A213390

KEYWORD

nonn,easy

AUTHOR

J. M. Bergot, Jun 28 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 04:29 EST 2022. Contains 358649 sequences. (Running on oeis4.)