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A213387
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a(n) = 5*2^(n-1) - 2 - 3*n.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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FORMULA
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G.f.: x^2*(2+x) / ( (1-2*x)*(1-x)^2 ). - R. J. Mathar, Jun 29 2012
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3); a(1)=0, a(2)=2, a(3)=9. - Harvey P. Dale, Sep 28 2012
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EXAMPLE
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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.
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MATHEMATICA
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Table[5*2^(n-1)-2-3n, {n, 30}] (* or *) LinearRecurrence[{4, -5, 2}, {0, 2, 9}, 30] (* Harvey P. Dale, Sep 28 2012 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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