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A219795
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Sum of the absolute values of the antidiagonals of the triangle A135929(n) companion. See the comment.
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3
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2, 2, 2, 2, 3, 3, 5, 7, 10, 11, 16, 23, 33, 44, 58, 81, 114, 158, 212, 293, 407, 565, 777, 1064, 1471, 2036, 2813, 3863, 5334, 7370, 10183, 14046, 19356, 26726, 36909, 50955, 70251, 96977, 133886, 184841, 255092
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OFFSET
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0,1
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COMMENTS
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The companion to A135929(n) is the triangle
2;
2, 0;
2, 0, 1;
2, 0, -1, 0;
2, 0, -3, 0, -1;
2, 0, -5, 0, 0, 0;
2, 0, -7, 0, 3, 0, 1;
2, 0, -9, 0, 8, 0, 1, 0;
(A192011(n) beginning with 2 instead of -1).
Consider a(1),a(5),a(10),a(14), that is, a(A193910(n) -1).
a(1)+a(4)-a(5) = 2, a(5)+a(8)-a(9) = 2, a(10)+a(13)-a(14) = 2, a(14)+a(17)-a(18) = 4, a(19)+a(22)-a(23) = 6, a(23)+a(26)-a(27) = 14, yields 2,2,2,4,6,14,24,60,... = 2*A047749(n) or 2, followed with A116637(n+1).
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LINKS
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FORMULA
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a(n) = sum abs ( [k=0..floor(n/2)] A192011(n-k,k) ), a(0)=2.
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EXAMPLE
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a(0)=2, a(1)=2, a(2)=2+0, a(3)=2+0, a(4)=2+0+1, a(5)=2+0+1.
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MAPLE
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if n=0 then
2;
else
add(abs(A192011(n-k, k)), k=0..floor(n/2)) ;
end if;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(24)-a(40) from Jean-Francois Alcover, Nov 28 2012
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STATUS
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approved
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