cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A210540 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 3 times.

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 8, 17, 40, 104, 291, 857, 2634, 8455, 28424, 100117, 368465, 1410903, 5599073, 22968514, 97267342, 424927846, 1913764155, 8877181958, 42358589064, 207639979365, 1044360973987, 5384167878948, 28429186870051, 153638182314504, 849295001319211
Offset: 0

Views

Author

R. H. Hardin, Mar 22 2012

Keywords

Examples

			Some solutions for n=11
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....1....1....1....0....1....1....1....1....1....1....1....1....0
..0....1....1....0....1....1....1....0....1....0....0....0....1....1....0....0
..1....1....0....1....0....1....1....0....1....1....0....1....1....1....1....1
..1....0....1....1....1....0....1....0....2....1....0....1....2....2....0....0
..2....2....0....2....2....2....0....0....0....1....1....0....1....2....0....0
..2....0....0....2....2....2....0....1....1....0....1....1....2....2....0....1
..2....1....0....1....0....1....2....0....1....0....2....0....2....2....1....1
..3....1....1....0....2....2....0....1....0....2....1....0....2....0....2....1

Links

Crossrefs

Column 3 of A210545.

Formula

a(n) = 1 if n<=3 else Sum_{i=0..n-3} binomial(n-3,i)*a(i). Proved by R. J. Mathar in the Sequence Fans Mailing List.

Extensions

a(0)=1 prepended by Alois P. Heinz, Apr 24 2023

A210541 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 4 times.

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 8, 16, 33, 73, 177, 467, 1309, 3813, 11409, 34999, 110510, 361194, 1226930, 4334048, 15877297, 60049447, 233426007, 929616461, 3786970033, 15777120457, 67260334185, 293617319221, 1312868943154, 6010792180952
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2012

Keywords

Comments

Column 4 of A210545

Examples

			Some solutions for n=13
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....0....1....1....1....0....1....1....0....0....1....0....0....1
..1....1....1....1....1....0....1....0....1....1....1....1....0....1....1....1
..0....1....0....0....1....0....1....0....0....0....0....1....0....0....1....0
..0....1....1....1....1....1....0....1....1....1....1....0....1....1....1....1
..1....2....1....0....0....1....1....1....1....1....0....0....1....1....1....0
..1....0....2....1....2....1....0....0....2....0....0....0....0....1....0....0
..0....1....1....1....2....2....1....1....1....0....0....1....0....2....2....1
..1....0....2....0....1....2....1....1....0....1....0....1....1....0....1....1
..2....0....1....2....1....0....2....2....2....0....0....1....2....0....2....0

Links

Formula

a(n) = 1 if n<=4 else sum{i=0..n-4}(binomial(n-4,i)*a(i)). Proved by R. J. Mathar in the Sequence Fans Mailing List.

A210542 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 5 times.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 65, 138, 315, 782, 2090, 5885, 17112, 50743, 152705, 466760, 1455562, 4658963, 15392116, 52663709, 186632887, 683133153, 2570929570, 9900731604, 38864321047, 155126476313, 629028834312, 2592051975917
Offset: 1

Views

Author

R. H. Hardin, Mar 22 2012

Keywords

Examples

			Some solutions for n=15:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....0....0....1....1....0....1....0....1....1....1....0....1....1....1
..0....0....0....0....0....0....1....1....1....0....1....0....0....1....1....0
..1....1....0....1....1....1....1....1....0....1....1....1....1....1....1....0
..0....0....1....0....1....0....1....0....0....1....0....0....1....1....1....1
..1....0....1....1....0....1....1....1....1....1....0....0....0....1....1....0
..0....0....1....1....0....1....1....1....1....1....0....0....1....1....1....1
..0....1....0....0....1....1....1....2....1....0....1....0....1....2....0....1
..0....0....0....0....0....2....1....0....1....1....1....1....1....2....1....0
..0....1....1....1....0....2....1....1....0....0....0....1....1....0....0....0
..0....0....1....1....0....0....1....0....1....1....0....0....2....2....0....1

Links

Crossrefs

Column 5 of A210545.

Formula

a(n) = 1 if n <= 5; otherwise, Sum_{i=0..n-5} binomial(n-5,i)*a(i). Proved by R. J. Mathar in the Sequence Fans Mailing List.

A210543 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 6 times.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 129, 267, 582, 1364, 3454, 9338, 26429, 76929, 227579, 680113, 2050000, 6242818, 19284165, 60754153, 196341570, 654012814, 2251195713, 8005274899, 29325473071, 110181281435, 422565983725
Offset: 1

Views

Author

R. H. Hardin, formula proved by R. J. Mathar in the Sequence Fans Mailing List, Mar 22 2012

Keywords

Examples

			Some solutions for n=17
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....0....0....1....1....1....0....1....1....1....1....0....0
..1....0....0....1....0....1....1....1....1....1....0....1....0....1....1....1
..0....0....0....1....1....1....1....0....1....1....1....0....1....1....1....1
..1....1....1....0....0....1....0....1....1....1....1....0....1....0....1....1
..0....0....1....1....0....1....1....1....0....0....0....0....0....1....1....1
..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
..0....1....0....0....1....0....0....1....1....1....1....1....1....1....1....0
..1....1....0....1....0....1....0....1....2....1....1....1....1....0....0....1
..1....0....0....1....1....0....1....0....2....1....0....0....0....0....1....1
..1....0....1....1....0....0....2....1....0....1....0....0....0....0....1....1
..2....0....1....0....1....0....1....1....2....0....0....1....2....1....2....0

Links

Crossrefs

Column 6 of A210545.

Formula

a(n) = 1 if n<=6 else Sum_{i=0..n-6} (binomial(n-6,i)*a(i)).

A210544 Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 7 times.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 257, 524, 1106, 2470, 5924, 15262, 41690, 118595, 345861, 1023028, 3050590, 9146312, 27567958, 83678750, 256632743, 798853376, 2537255097, 8264988956, 27723246374, 95941707086, 342355797248
Offset: 1

Views

Author

R. H. Hardin, formula proved by R. J. Mathar in the Sequence Fans Mailing List, Mar 22 2012

Keywords

Comments

Column 7 of A210545.

Examples

			Some solutions for n=19
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....0....1....1....0....1....1....1....1....0....1....0....0....0
..1....1....0....0....0....1....1....0....0....1....1....1....0....1....1....1
..1....0....1....1....1....0....1....0....0....1....0....0....0....1....0....1
..0....1....0....0....0....1....1....0....1....1....1....1....0....1....1....1
..0....0....1....0....1....0....1....0....1....0....1....0....0....1....1....0
..1....0....0....1....1....1....0....0....0....1....1....0....1....1....1....0
..0....1....1....0....1....1....0....0....0....1....1....1....0....1....1....0
..0....1....1....0....1....1....0....0....1....0....1....0....0....1....1....1
..1....1....1....1....0....1....0....0....1....1....2....1....1....0....1....0
..1....1....1....1....0....2....0....0....0....1....1....1....1....0....2....1
..0....0....1....1....1....1....0....0....1....0....1....1....0....1....2....1
..0....1....1....1....0....2....1....1....1....0....0....0....1....1....2....1

Links

Crossrefs

Cf. A210545.

Formula

a(n) = 1 if n<=7 else Sum_{i=0..n-7} binomial(n-7,i)*a(i).
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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