A316723 -id:A316723 - cp's OEIS frontend

A069251 Number of basis partitions of n+64 with Durfee square size 8.

1, 2, 4, 8, 14, 24, 40, 64, 100, 152, 226, 330, 474, 670, 934, 1286, 1748, 2350, 3128, 4122, 5384, 6974, 8960, 11426, 14468, 18196, 22740, 28248, 34888, 42854, 52366, 63670, 77048, 92816, 111324, 132970, 158194, 187482, 221380, 260488, 305466

Offset: 0

Benoit Cloitre, Apr 13 2002

Seiichi Manyama, Table of n, a(n) for n = 0..10000
M. D. Hirschhorn, Basis partitions and Rogers-Ramanujan partitions, Discrete Math. 205 (1999), 241-243.

Column k=8 of A316723.

s=8; a(n)=polcoeff(prod(i=1,s,(1+x^i))/(prod(i=1,s,(1-x^i))+x*O(x^n)),n) for(n=0,50,print1(a(n),","))

G.f.: (x^4 -x^3 +x^2 -x +1)*(x^4 -x^2 +1)*(x^6 -x^5 +x^4 -x^3 +x^2 -x +1)*(x^8 +1)/((x -1)^8*(x^2 +x +1)^2*(x^4 +x^3 +x^2 +x +1)*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). [Colin Barker, Sep 23 2012]

A069252 Number of basis partitions of n+81 with Durfee square size 9.

Original entry on oeis.org

1, 2, 4, 8, 14, 24, 40, 64, 100, 154, 230, 338, 490, 698, 982, 1366, 1876, 2550, 3434, 4578, 6052, 7938, 10328, 13342, 17120, 21820, 27640, 34810, 43588, 54290, 67278, 82958, 101816, 124404, 151340, 183350, 221252, 265958, 318524, 380132, 452094

Offset: 0

Benoit Cloitre, Apr 13 2002

Seiichi Manyama, Table of n, a(n) for n = 0..10000
M. D. Hirschhorn, Basis partitions and Rogers-Ramanujan partitions, Discrete Math. 205 (1999), 241-243.

Column k=9 of A316723.

s=9; a(n)=polcoeff(prod(i=1,s,(1+x^i))/(prod(i=1,s,(1-x^i))+x*O(x^n)),n) for(n=0,50,print1(a(n),","))

G.f.: -(x +1) * (x^2 -x +1) * (x^4 -x^3 +x^2 -x +1) * (x^4 -x^2 +1) * (x^6 -x^5 +x^4 -x^3 +x^2 -x +1) * (x^6 -x^3 +1) * (x^8 +1) / ((x -1)^9 * (x^2 +x +1)^3 * (x^4 +x^3 +x^2 +x +1) * (x^6 +x^3 +1) * (x^6 +x^5 +x^4 +x^3 +x^2 +x +1)). - Colin Barker, Jul 13 2013

A069253 Number of basis partitions of n+100 with Durfee square size 10.

Original entry on oeis.org

1, 2, 4, 8, 14, 24, 40, 64, 100, 154, 232, 342, 498, 714, 1010, 1414, 1956, 2678, 3634, 4886, 6514, 8618, 11316, 14754, 19112, 24600, 31472, 40038, 50656, 63754, 79844, 99514, 123460, 152500, 187572, 229770, 280364, 340806, 412768, 498176, 599216

Offset: 0

Benoit Cloitre, Apr 13 2002

Seiichi Manyama, Table of n, a(n) for n = 0..10000
M. D. Hirschhorn, Basis partitions and Rogers-Ramanujan partitions, Discrete Math. 205 (1999), 241-243.

Column k=10 of A316723.

s=10; a(n)=polcoeff(prod(i=1,s,(1+x^i))/(prod(i=1,s,(1-x^i))+x*O(x^n)),n)
for(n=0,50,print1(a(n),","))

G.f.: (x^2 -x +1) * (x^2 +1) * (x^4 -x^2 +1) * (x^6 -x^5 +x^4 -x^3 +x^2 -x +1) * (x^6 -x^3 +1) * (x^8 -x^6 +x^4 -x^2 +1) * (x^8 +1) / ((x -1)^10 * (x^2 +x +1)^3 * (x^4 +x^3 +x^2 +x +1)^2 * (x^6 +x^3 +1) * (x^6 +x^5 +x^4+ x^3 +x^2 +x +1)). - Colin Barker, Jul 13 2013

cp's OEIS Frontend

A069251 Number of basis partitions of n+64 with Durfee square size 8.

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A069252 Number of basis partitions of n+81 with Durfee square size 9.

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PARI

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A069253 Number of basis partitions of n+100 with Durfee square size 10.

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Author

Keywords

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Programs

PARI

Formula