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A156224 Triangle read by rows:t(n,m)=(Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2. 0
1, 1, 1, 1, 4, 1, 3, 10, 10, 3, 3, 18, 22, 18, 3, 5, 28, 58, 58, 28, 5, 7, 46, 103, 158, 103, 46, 7, 9, 68, 187, 313, 313, 187, 68, 9, 11, 94, 306, 614, 698, 614, 306, 94, 11, 15, 133, 502, 1174, 1636, 1636, 1174, 502, 133, 15, 19, 188, 763, 2038, 3358, 4030, 3358, 2038, 763 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 6, 26, 64, 182, 470, 1154, 2748, 6920, 16762,...}

LINKS

Table of n, a(n) for n=0..63.

FORMULA

t(n,m)=(Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2.

EXAMPLE

{1},

{1, 1},

{1, 4, 1},

{3, 10, 10, 3},

{3, 18, 22, 18, 3},

{5, 28, 58, 58, 28, 5},

{7, 46, 103, 158, 103, 46, 7},

{9, 68, 187, 313, 313, 187, 68, 9},

{11, 94, 306, 614, 698, 614, 306, 94, 11},

{15, 133, 502, 1174, 1636, 1636, 1174, 502, 133, 15},

{19, 188, 763, 2038, 3358, 4030, 3358, 2038, 763, 188, 19}

MATHEMATICA

Clear[t, n, m];

t[n_, m_] = (Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*( PartitionsQ[n - m] + PartitionsQ[m])) - 2;

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A321121 A093735 A298918 * A162516 A193793 A301510

Adjacent sequences:  A156221 A156222 A156223 * A156225 A156226 A156227

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 06 2009

STATUS

approved

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Last modified October 14 12:25 EDT 2019. Contains 328006 sequences. (Running on oeis4.)