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 A157522 Triangle read by rows: f(n,m)=1 + If[m <= floor[n/4], m, If[m > floor[n/4] && m <= floor[n/2], floor[n/2] - m, If[m > floor[n/2] && m <= floor[3*n/4], m - floor[n/2], n - m]]]; t(n,m)=f(n,m)+f(n,n-m)-1. then t(n,m)=f(n,m)+f(n,n-m)-1 0

%I

%S 1,1,1,1,1,1,1,2,2,1,1,3,1,3,1,1,3,2,2,3,1,1,3,3,1,3,3,1,1,3,4,2,2,4,

%T 3,1,1,3,5,3,1,3,5,3,1,1,3,5,4,2,2,4,5,3,1,1,3,5,5,3,1,3,5,5,3,1

%N Triangle read by rows: f(n,m)=1 + If[m <= floor[n/4], m, If[m > floor[n/4] && m <= floor[n/2], floor[n/2] - m, If[m > floor[n/2] && m <= floor[3*n/4], m - floor[n/2], n - m]]]; t(n,m)=f(n,m)+f(n,n-m)-1. then t(n,m)=f(n,m)+f(n,n-m)-1

%C Row sums are: {1, 2, 3, 6, 9, 12, 15, 20, 25, 30, 35,...}.

%C This is a bimodal tent function made to be like the collapsing middle binomial derivative.

%e {1},

%e {1, 1},

%e {1, 1, 1},

%e {1, 2, 2, 1},

%e {1, 3, 1, 3, 1},

%e {1, 3, 2, 2, 3, 1},

%e {1, 3, 3, 1, 3, 3, 1},

%e {1, 3, 4, 2, 2, 4, 3, 1},

%e {1, 3, 5, 3, 1, 3, 5, 3, 1},

%e {1, 3, 5, 4, 2, 2, 4, 5, 3, 1},

%e {1, 3, 5, 5, 3, 1, 3, 5, 5, 3, 1}

%t Clear[f, n, m];

%t f[n_, m_] = 1 + If[m <= Floor[n/4], m, If[m > Floor[n/4] && m <= Floor[n/2], Floor[n/2] - m, If[m > Floor[n/2] && m <= Floor[3*n/4], m - Floor[n/2], n - m]]];

%t Table[Table[f[n, m] + f[n, n - m] - 1, {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn,tabl

%O 0,8

%A _Roger L. Bagula_, Mar 02 2009

%E Edited by _N. J. A. Sloane_, Mar 05 2009

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Last modified December 7 12:17 EST 2021. Contains 349581 sequences. (Running on oeis4.)