A156044 - OEIS

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A156044

A triangle sequence made symmetrical by reverse coefficients: t0(n,m)=2 + PartitionsP[n] - PartitionsP[m] - PartitionsP[n - m]; t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 3, 3, 1, 1, 3, 4, 4, 3, 1, 1, 5, 6, 7, 6, 5, 1, 1, 5, 8, 9, 9, 8, 5, 1, 1, 8, 11, 14, 14, 14, 11, 8, 1, 1, 9, 15, 18, 20, 20, 18, 15, 9, 1, 1, 13, 20, 26, 28, 30, 28, 26, 20, 13, 1

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

OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 4, 6, 11, 16, 31, 46, 82, 126, 206,...}.

The idea here was tom design a symmetrical analog of a Pascal's triangle using p

partitions and addition and subtraction instead of multiplication.

LINKS

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

FORMULA

t0(n,m)=2 + PartitionsP[n] - PartitionsP[m] - PartitionsP[n - m];

t(n,m)=(t0(n,m)+Reverse[t0(n,m)])/2

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 2, 2, 1},

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

{1, 3, 4, 4, 3, 1},

{1, 5, 6, 7, 6, 5, 1},

{1, 5, 8, 9, 9, 8, 5, 1},

{1, 8, 11, 14, 14, 14, 11, 8, 1},

{1, 9, 15, 18, 20, 20, 18, 15, 9, 1},

{1, 13, 20, 26, 28, 30, 28, 26, 20, 13, 1}

MATHEMATICA

Clear[t];

t[n_, m_] = 2 + PartitionsP[n] - PartitionsP[m] - PartitionsP[n - m];

Table[(Table[t[n, m], {m, 0, n}] + Reverse[Table[t[n, m], {m, 0, n}]])/2, {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A103441 A081206 A333161 * A180980 A275298 A048570

Adjacent sequences: A156041 A156042 A156043 * A156045 A156046 A156047

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 02 2009

STATUS

approved