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A213387 a(n) = 5*2^(n-1)-2-3*n. 1
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

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Last modified June 24 08:22 EDT 2017. Contains 288697 sequences.