A225010 -id:A225010 - cp's OEIS frontend

A225013 Number of 6Xn 0..1 arrays with rows unimodal and columns nondecreasing.

7, 49, 252, 1036, 3612, 11088, 30738, 78354, 186142, 416394, 884236, 1794196, 3497248, 6577474, 11980667, 21201211, 36548573, 61520899, 101320712, 163556776, 259187048, 403770544, 619111172, 935394436, 1393938716, 2050706932

Offset: 1

R. H. Hardin Apr 23 2013

nonn

Row 6 of A225010

			Some solutions for n=3
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..1..0....1..1..0
..0..1..0....0..0..0....0..1..0....0..0..0....0..0..0....0..1..1....1..1..0
..0..1..0....1..0..0....0..1..1....0..1..0....1..0..0....0..1..1....1..1..0
..0..1..0....1..1..0....0..1..1....0..1..0....1..0..0....0..1..1....1..1..0
..1..1..0....1..1..0....1..1..1....0..1..0....1..0..0....0..1..1....1..1..1
..1..1..1....1..1..0....1..1..1....0..1..0....1..0..0....1..1..1....1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/479001600)*n^12 + (1/7257600)*n^11 + (187/43545600)*n^10 + (13/161280)*n^9 + (14671/14515200)*n^8 + (3043/345600)*n^7 + (2380201/43545600)*n^6 + (347911/1451520)*n^5 + (8129699/10886400)*n^4 + (923183/604800)*n^3 + (913741/415800)*n^2 + (49/40)*n + 1

A225014 Number of 7Xn 0..1 arrays with rows unimodal and columns nondecreasing.

Original entry on oeis.org

8, 64, 372, 1716, 6672, 22716, 69498, 194634, 505912, 1233584, 2845492, 6251596, 13154948, 26635774, 52097267, 98759971, 181971248, 326703424, 572756312, 982365976, 1651162688, 2723729944, 4415408372, 7042481236, 11063492816

Offset: 1

R. H. Hardin Apr 23 2013

nonn

Row 7 of A225010

			Some solutions for n=3
..1..1..0....0..0..1....0..1..0....1..0..0....0..0..0....0..0..0....0..0..0
..1..1..0....0..0..1....1..1..0....1..0..0....0..1..0....0..0..0....0..1..0
..1..1..0....0..0..1....1..1..0....1..1..0....1..1..0....0..0..0....0..1..0
..1..1..0....0..0..1....1..1..0....1..1..0....1..1..0....0..0..1....1..1..0
..1..1..0....0..0..1....1..1..1....1..1..0....1..1..0....0..0..1....1..1..0
..1..1..0....0..1..1....1..1..1....1..1..1....1..1..1....0..1..1....1..1..0
..1..1..0....0..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = (1/87178291200)*n^14 + (1/958003200)*n^13 + (43/958003200)*n^12 + (103/87091200)*n^11 + (1847/87091200)*n^10 + (7891/29030400)*n^9 + (1560493/609638400)*n^8 + (222427/12441600)*n^7 + (2023297/21772800)*n^6 + (1926401/5443200)*n^5 + (29332549/29937600)*n^4 + (1353853/739200)*n^3 + (183490757/75675600)*n^2 + (363/280)*n + 1

A228510 a(n) = (128n^4/25+14528n^3/225+20344n^2/75+661816n/1575+168)*(n+6)!/n!.

Original entry on oeis.org

120960, 4682880, 54268416, 364571136, 1758756096, 6759726336, 21978671616, 62815154688, 161990345088, 384087420288, 849090198528, 1768911326208, 3502103394816, 6633368787456, 12086145432576, 21278464551936, 36334471510656, 60366490588800

Offset: 0

Charles A. Lane, Aug 23 2013

Name was "Coefficients from quartic oscillator number 22".

See comment and example in A225010.

			For n=4 the solution is 1758756096.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A225010.

m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1152*(105+2910*x+8168*x^2+4530*x^3+415*x^4)/(1-x)^11)); // Bruno Berselli, Oct 16 2013

Table[(128 n^4/25 + 14528 n^3/225 + 20344 n^2/75 + 661816 n/1575 + 168) (n + 6)!/n!, {n, 0, 20}] (* Bruno Berselli, Oct 16 2013 *)

G.f.: 1152*(105 +2910*x +8168*x^2 +4530*x^3 +415*x^4)/(1-x)^11. [Bruno Berselli, Oct 16 2013]

cp's OEIS Frontend

A225013 Number of 6Xn 0..1 arrays with rows unimodal and columns nondecreasing.

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A225014 Number of 7Xn 0..1 arrays with rows unimodal and columns nondecreasing.

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Keywords

Comments

Examples

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Formula

A228510 a(n) = (128n^4/25+14528n^3/225+20344n^2/75+661816n/1575+168)*(n+6)!/n!.

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cp's OEIS Frontend

A225013 Number of 6Xn 0..1 arrays with rows unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A225014 Number of 7Xn 0..1 arrays with rows unimodal and columns nondecreasing.

Views

Author

Keywords

Comments

Examples

Links

Formula

A228510 a(n) = (128*n^4/25+14528*n^3/225+20344*n^2/75+661816*n/1575+168)*(n+6)!/n!.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A228510 a(n) = (128n^4/25+14528n^3/225+20344n^2/75+661816n/1575+168)*(n+6)!/n!.