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A172281 Asymmetrical triangle form:l=1;t(n,k,l)=Ceiling[Binomial[n, k]*(l + 1)/((1 + l)^2 + (k - Floor[n/2])^2)] 0
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 5, 4, 2, 1, 1, 2, 6, 10, 6, 2, 1, 1, 2, 9, 18, 14, 6, 2, 1, 1, 2, 7, 23, 35, 23, 7, 2, 1, 1, 2, 9, 34, 63, 51, 21, 6, 1, 1, 1, 1, 7, 30, 84, 126, 84, 30, 7, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 2, 3, 6, 9, 15, 28, 53, 101, 189, 372,...}.

This function was constructed to impose a "S" shape on a binomial triangle.

LINKS

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

FORMULA

l=1;

t(n,k,l)=Ceiling[Binomial[n, k]*(l + 1)/((1 + l)^2 + (k - Floor[n/2])^2)]

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, 2, 2, 1},

{1, 2, 3, 2, 1},

{1, 2, 5, 4, 2, 1},

{1, 2, 6, 10, 6, 2, 1},

{1, 2, 9, 18, 14, 6, 2, 1},

{1, 2, 7, 23, 35, 23, 7, 2, 1},

{1, 2, 9, 34, 63, 51, 21, 6, 1, 1},

{1, 1, 7, 30, 84, 126, 84, 30, 7, 1, 1}

MATHEMATICA

T[n_, k_, l_]=Ceiling[Binomial[n, k]*(l+1)/((1+l)^2+(k-Floor[n/2])^2)];

Table[Table[Table[T[n, k, l], {k, 0, n}], {n, 0, 10}], {l, 0, 5}];

Table[Flatten[Table[Table[T[n, k, l], {k, 0, n}], {n, 0, 10}]], {l, 0, 5}]

CROSSREFS

Sequence in context: A103343 A085263 A115092 * A304945 A176298 A259575

Adjacent sequences:  A172278 A172279 A172280 * A172282 A172283 A172284

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 30 2010

STATUS

approved

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Last modified November 22 08:46 EST 2019. Contains 329389 sequences. (Running on oeis4.)