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A176346 A dual remainder symmetrical triangle sequence T(n, m) = 1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)*floor((n+1)/( n-m+1)), read by rows. 2

%I

%S 1,1,1,1,3,1,1,2,2,1,1,3,5,3,1,1,2,3,3,2,1,1,3,4,7,4,3,1,1,2,5,4,4,5,

%T 2,1,1,3,3,5,9,5,3,3,1,1,2,4,6,5,5,6,4,2,1,1,3,5,7,6,11,6,7,5,3,1,1,2,

%U 3,4,7,6,6,7,4,3,2,1,1,3,4,5,8,7,13,7,8,5,4,3,1

%N A dual remainder symmetrical triangle sequence T(n, m) = 1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)*floor((n+1)/( n-m+1)), read by rows.

%C This sequence comes from computability functions.

%C Row sums are : {1, 2, 5, 6, 13, 12, 23, 24, 33, 36, 55,...}.

%D N. J. Cutland, "Computability, An introduction to recursive function theory", Cambridge University Press, London, 1980, page 37.

%D Martin Davis, "Computability and Unsolvability", Dover Press, New York, page 43.

%H G. C. Greubel, <a href="/A176346/b176346.txt">Rows n = 0..100 of triangle, flattened</a>

%F T(n, m) = 1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)*floor((n+1)/( n-m+1)).

%e Triangle begins as:

%e 1;

%e 1, 1;

%e 1, 3, 1;

%e 1, 2, 2, 1;

%e 1, 3, 5, 3, 1;

%e 1, 2, 3, 3, 2, 1;

%e 1, 3, 4, 7, 4, 3, 1;

%e 1, 2, 5, 4, 4, 5, 2, 1;

%e 1, 3, 3, 5, 9, 5, 3, 3, 1;

%e 1, 2, 4, 6, 5, 5, 6, 4, 2, 1;

%e 1, 3, 5, 7, 6, 11, 6, 7, 5, 3, 1;

%t T[n_, m_]:= 3 +2*n -(m+1)*Floor[(n+1)/(m+1)] -(n-m+1)*Floor[(n+1)/(n-m+1 )]; Table[T[n, m], {n,0,12}, {m,0,n}]//Flatten (* modified by _G. C. Greubel_, Apr 26 2019 *)

%o (PARI) {T(n,m) = 1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)* floor((n+1)/(n-m+1))}; \\ _G. C. Greubel_, Apr 26 2019

%o (MAGMA) [[1 + 2*(n+1) - (m+1)*Floor((n+1)/(m+1)) - (n-m+1)*Floor((n+1)/( n-m+1)): m in [0..n]]: n in [0..12]]; // _G. C. Greubel_, Apr 26 2019

%o (Sage) [[1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)*floor((n+1)/( n-m+1)) for m in (0..n)] for n in (0..12)] # _G. C. Greubel_, Apr 26 2019

%Y Cf. A176298.

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Apr 15 2010

%E Edited by _G. C. Greubel_, Apr 26 2019

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Last modified October 21 17:37 EDT 2021. Contains 348155 sequences. (Running on oeis4.)