A200251 T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo (k+1)

2, 3, 3, 4, 6, 5, 5, 10, 12, 8, 6, 15, 26, 24, 13, 7, 21, 45, 69, 48, 21, 8, 28, 75, 135, 181, 96, 34, 9, 36, 112, 267, 405, 476, 192, 55, 10, 45, 164, 448, 951, 1215, 1252, 384, 89, 11, 55, 225, 750, 1792, 3387, 3645, 3292, 768, 144, 12, 66, 305, 1125, 3434, 7168, 12063

Offset

1,1

Comments

Table starts

...2....3.....4.....5......6.......7.......8........9.......10........11

...3....6....10....15.....21......28......36.......45.......55........66

...5...12....26....45.....75.....112.....164......225......305.......396

...8...24....69...135....267.....448.....750.....1125.....1690......2376

..13...48...181...405....951....1792....3434.....5625.....9365.....14256

..21...96...476..1215...3387....7168...15724....28125....51895.....85536

..34..192..1252..3645..12063...28672...71970...140625...287570....513216

..55..384..3292.10935..42963..114688..329455...703125..1593535...3079296

..89..768..8657.32805.153015..458752.1508139..3515625..8830385..18475776

.144.1536.22765.98415.544971.1835008.6903702.17578125.48932530.110854656

Links

R. H. Hardin, Table of n, a(n) for n = 1..9999

Formula

Empirical: T(n,2k) = (2*k+1)*(k+1)^(n-1)

Example

Some solutions for n=7 k=6
..1....2....4....0....1....0....4....0....1....4....2....3....1....3....3....3
..3....5....6....3....2....6....5....4....1....5....5....4....2....5....3....4
..4....5....5....6....5....6....5....6....6....2....1....0....5....6....6....1
..6....5....3....2....6....5....3....6....2....5....3....0....3....0....6....1
..2....5....6....6....0....6....4....3....5....2....5....5....4....2....5....5
..6....2....5....6....2....2....2....5....2....4....5....5....4....5....6....2
..5....4....1....3....4....4....2....5....3....3....1....3....6....1....6....5

Crossrefs

Column 1 is A000045(n+2)

Column 2 is A003945

Column 3 is A099234(n+1)

Column 4 is A005030(n-1)

Column 6 is A002042(n-1)

Row 2 is A000217(n+1)

Sequence in context: A282442 A200668 A200469 * A207100 A281365 A304705

Adjacent sequences: A200248 A200249 A200250 * A200252 A200253 A200254

Keyword

nonn,tabl

Author

R. H. Hardin Nov 15 2011

Status

approved