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A193911
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Sums of the diagonals of the matrix formed by listing the h-Stohr sequences in increasing order.
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2
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1, 3, 7, 14, 25, 43, 69, 110, 167, 255, 375, 558, 805, 1179, 1681, 2438, 3451, 4975, 7011, 10070, 14153, 20283, 28461, 40734, 57103, 81663, 114415, 163550, 229069, 327355, 458409, 654998, 917123, 1310319, 1834587, 2620998, 3669553, 5242395, 7339525, 10485230
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OFFSET
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1,2
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LINKS
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FORMULA
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All h-Stohr sequences have formula: h terms 1,2,..,2^(n-1),..,2^(h-1) and then continue (2^h-1)(n-h)+1. - Henry Bottomley, Feb 04 2000
So we get the sums from the piecewise function:
for odd n>=1, a(n)=2^((n+1)/2)-n+((n+1)/2)-2+Sum_{i=0..((n+1)/2)-1}(2*i+1)*(2^(((n+1)/2)-i) -1);
for even n>=2, a(n)=2^((n/2)+2)-n-4+Sum_{i=0..(n/2)-1}(2*i+1)*(2^((n/2)-i) -1). - Jeffrey R. Goodwin, Aug 09 2011
a(n) = 1/8*(2^(n/2+2)*((10-7*sqrt(2))*(-1)^n+10+7*sqrt(2))-(-1)^n-2*n*(n+12)-79). - _Alexander R. Povolotsky, Aug 09 2011
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EXAMPLE
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Portion of the first three rows:
Thus a(1)=1, a(2)=2+1=3, and a(3)=4+2+1=7.
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MATHEMATICA
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LinearRecurrence[{2, 2, -6, 1, 4, -2}, {1, 3, 7, 14, 25, 43}, 40] (* Harvey P. Dale, Jun 20 2015 *)
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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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