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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
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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

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

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

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

{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, 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}

MATHEMATICA

Clear[f, n, m];

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]]];

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

Flatten[%]

CROSSREFS

Sequence in context: A338117 A184305 A337279 * A059674 A342748 A117545

Adjacent sequences:  A157519 A157520 A157521 * A157523 A157524 A157525

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Mar 02 2009

EXTENSIONS

Edited by N. J. A. Sloane, Mar 05 2009

STATUS

approved

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Last modified October 21 10:40 EDT 2021. Contains 348150 sequences. (Running on oeis4.)