A200942 -id:A200942 - cp's OEIS frontend

A200939 Number of 0..3 arrays x(0..n-1) of n elements with nondecreasing average value and 0..3 occur with instance counts within one of each other.

4, 6, 7, 3, 17, 40, 46, 21, 135, 342, 402, 186, 1240, 3225, 3850, 1785, 12220, 32333, 39011, 18123, 126294, 338016, 410508, 190974, 1347066, 3634200, 4433652, 2064492, 14694240, 39879609, 48816834, 22746537, 163035180, 444514785, 545548575

Offset: 1

R. H. Hardin Nov 24 2011

nonn

Column 3 of A200942

			Some solutions for n=8
..0....0....0....0....0....0....0....0....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....2....2....2....1....1....3....1....2....1....1....3....1....3....1....2
..1....1....1....1....3....1....1....2....2....1....3....1....1....1....1....1
..3....1....1....1....1....2....1....1....1....2....1....1....3....1....3....2
..2....2....3....3....3....2....2....2....1....3....2....3....3....2....2....1
..3....3....2....3....2....3....3....3....3....2....3....2....2....2....2....3
..2....3....3....2....2....3....2....3....3....3....2....2....2....3....3....3

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

A200940 Number of 0..4 arrays x(0..n-1) of n elements with nondecreasing average value and 0..4 occur with instance counts within one of each other.

Original entry on oeis.org

5, 10, 17, 15, 8, 61, 206, 410, 426, 228, 1990, 7716, 16748, 18500, 10280, 91970, 366650, 807790, 898170, 494900, 4595290, 18895520, 42353066, 47612754, 26290908, 249098136, 1045149420, 2370753798, 2686351206, 1487368344, 14257307064

Offset: 1

R. H. Hardin Nov 24 2011

nonn

Column 4 of A200942

			Some solutions for n=8
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....1....0....2....2....0....0....0....1....0....1....0....0....0....0
..1....1....1....1....1....1....1....1....1....1....1....4....1....1....3....2
..4....1....4....1....1....1....1....2....4....3....1....2....4....2....1....1
..2....4....2....2....4....3....3....2....3....2....2....3....3....4....2....1
..3....4....3....4....3....4....3....4....2....3....4....2....2....3....4....2
..3....3....2....4....3....2....4....3....3....2....3....3....4....2....3....3
..2....2....3....3....4....4....2....4....4....4....4....4....3....4....2....4

R. H. Hardin, Table of n, a(n) for n = 1..207

A200941 Number of 0..7 arrays x(0..n-1) of n elements with nondecreasing average value and 0..7 occur with instance counts within one of each other.

Original entry on oeis.org

8, 28, 90, 213, 398, 536, 496, 212, 3748, 31522, 162688, 559147, 1311219, 2029362, 1882767, 803904, 17367570, 171263266, 1001635722, 3786706210, 9461740656, 15221077360, 14401078980, 6125881940, 143992454820, 1520973953255

Offset: 1

R. H. Hardin Nov 24 2011

nonn

Column 7 of A200942

			Some solutions for n=8
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....2....2....1....1....1....1....2....1....1....2....2
..4....2....2....3....2....1....1....2....2....2....3....1....4....2....1....1
..3....4....5....2....5....4....6....5....3....4....4....3....2....6....5....4
..2....3....3....5....4....6....3....4....4....5....2....7....5....3....4....5
..7....5....4....7....6....5....5....3....6....3....7....6....3....4....3....3
..5....6....6....6....3....3....7....7....5....6....5....4....7....5....6....6
..6....7....7....4....7....7....4....6....7....7....6....5....6....7....7....7

R. H. Hardin, Table of n, a(n) for n = 1..58

A200943 Number of 0..n arrays x(0..3) of 4 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

Original entry on oeis.org

1, 7, 3, 15, 46, 107, 213, 383, 636, 997, 1492, 2151, 3005, 4092, 5447, 7114, 9135, 11559, 14433, 17814, 21753, 26313, 31552, 37538, 44334, 52016, 60651, 70321, 81100, 93075, 106325, 120945, 137018, 154645, 173916, 194937, 217803, 242628, 269511

Offset: 1

R. H. Hardin Nov 24 2011

nonn

Row 4 of A200942

			Some solutions for n=8
..1....1....0....1....0....0....1....2....1....3....1....2....4....0....0....1
..7....3....1....2....1....1....4....5....6....7....4....4....5....2....2....4
..6....2....2....3....5....6....5....4....4....5....5....7....8....8....4....6
..8....4....5....8....4....7....6....8....8....8....7....8....7....4....8....8

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

Empirical: a(n) = 2*a(n-1) +a(n-2) -3*a(n-3) -a(n-4) +a(n-5) +3*a(n-6) -a(n-7) -2*a(n-8) +a(n-9) for n>11

Empirical g.f.: x+7x^2 -x^3*(3+9*x+13*x^2+x^4+9*x^3) / ( (1+x+x^2)*(1+x)^2*(x-1)^5 ). - R. J. Mathar, Nov 25 2011

A200944 Number of 0..n arrays x(0..4) of 5 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

Original entry on oeis.org

2, 9, 17, 8, 44, 151, 398, 890, 1774, 3246, 5555, 9016, 14012, 21005, 30529, 43228, 59824, 81159, 108166, 141927, 183608, 234553, 296197, 370168, 458195, 562234, 684319, 826757, 991940, 1182536, 1401309, 1651348, 1935801, 2258191, 2622105

Offset: 1

R. H. Hardin Nov 24 2011

nonn

Row 5 of A200942.

			Some solutions for n=8
..0....0....0....0....0....1....0....1....0....1....0....0....0....0....1....2
..2....2....1....1....2....2....2....2....2....2....4....4....5....1....2....4
..7....7....3....8....1....8....3....5....1....5....2....5....3....3....5....5
..3....4....2....5....6....4....4....4....4....7....7....3....6....4....6....6
..4....5....6....7....8....7....5....3....7....8....5....8....4....2....8....7

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

Cf. A200942.

Empirical: a(n) = 2*a(n-2) +2*a(n-3) -a(n-4) -3*a(n-5) -a(n-6) +a(n-8) +a(n-9) +a(n-10) -a(n-11) -a(n-12) +a(n-13) +a(n-14) +a(n-15) -a(n-17) -3*a(n-18) -a(n-19) +2*a(n-20) +2*a(n-21) -a(n-23) for n>26.

Empirical g.f.: 2*x +9*x^2 +17*x^3 +x^4*(8+44*x +135*x^2+294*x^3 +508*x^4+744*x^5 +961*x^6+1122*x^7 +1203*x^8+1200*x^9 +1118*x^10+955*x^11 +734*x^12+496*x^13 +289*x^14+128*x^15 +35*x^16+x^17) / ( (x^2+1)*(x^4+x^3+x^2+x+1)*(x^4+1)*(1+x+x^2)^2*(1+x)^3*(x-1)^6 ). - R. J. Mathar, Nov 25 2011

A200945 Number of 0..n arrays x(0..5) of 6 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

Original entry on oeis.org

1, 6, 40, 61, 20, 134, 536, 1613, 4023, 8842, 17681, 32835, 57465, 95825, 153352, 237104, 355792, 520226, 743448, 1041280, 1432241, 1938480, 2585494, 3403125, 4425342, 5691528, 7245651, 9138376, 11425775, 14171497, 17445655, 21327385

Offset: 1

R. H. Hardin Nov 24 2011

nonn

Row 6 of A200942

			Some solutions for n=8
..2....0....0....0....0....0....0....0....0....0....0....0....0....0....1....1
..3....1....2....2....2....2....2....1....1....2....5....1....2....4....2....4
..4....4....1....1....3....7....6....7....7....1....6....4....1....2....3....8
..5....3....4....7....5....3....3....4....5....8....4....2....4....6....5....5
..8....7....5....4....6....6....4....3....8....5....8....8....6....5....6....7
..7....8....8....8....8....4....5....8....6....6....7....5....8....8....8....6

R. H. Hardin, Table of n, a(n) for n = 1..143

Empirical: a(n) = -a(n-1) -a(n-2) +a(n-6) +2*a(n-7) +4*a(n-8) +3*a(n-9) +3*a(n-10) +2*a(n-11) +2*a(n-12) -3*a(n-14) -4*a(n-15) -5*a(n-16) -5*a(n-17) -7*a(n-18) -7*a(n-19) -5*a(n-20) -2*a(n-21) +3*a(n-24) +6*a(n-25) +8*a(n-26) +7*a(n-27) +6*a(n-28) +7*a(n-29) +7*a(n-30) +5*a(n-31) +a(n-32) -a(n-35) -5*a(n-36) -7*a(n-37) -7*a(n-38) -6*a(n-39) -7*a(n-40) -8*a(n-41) -6*a(n-42) -3*a(n-43) +2*a(n-46) +5*a(n-47) +7*a(n-48) +7*a(n-49) +5*a(n-50) +5*a(n-51) +4*a(n-52) +3*a(n-53) -2*a(n-55) -2*a(n-56) -3*a(n-57) -3*a(n-58) -4*a(n-59) -2*a(n-60) -a(n-61) +a(n-65) +a(n-66) +a(n-67) for n>71

A200946 Number of 0..n arrays x(0..6) of 7 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

Original entry on oeis.org

2, 22, 46, 206, 214, 70, 496, 2185, 7215, 19783, 47458, 102886, 206061, 386953, 688784, 1172655, 1921632, 3046700, 4693133, 7048602, 10349707, 14894334, 21049108, 29263715, 40081693, 54158684, 72270348, 95341262, 124450340

Offset: 1

R. H. Hardin Nov 24 2011

nonn

Row 7 of A200942

			Some solutions for n=8
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....2....3....2....2....1....2....3....2....2....1....1....1....1....2....1
..2....4....2....6....6....5....6....4....7....1....3....5....4....2....1....3
..3....8....5....4....7....3....4....7....3....4....7....2....3....7....5....2
..5....7....8....3....4....6....5....8....5....5....4....6....5....5....3....7
..4....5....6....8....8....4....8....6....6....6....6....8....6....6....6....5
..6....6....4....7....5....8....7....5....8....3....8....7....8....4....7....6

R. H. Hardin, Table of n, a(n) for n = 1..84

cp's OEIS Frontend

A200939 Number of 0..3 arrays x(0..n-1) of n elements with nondecreasing average value and 0..3 occur with instance counts within one of each other.

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A200940 Number of 0..4 arrays x(0..n-1) of n elements with nondecreasing average value and 0..4 occur with instance counts within one of each other.

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A200941 Number of 0..7 arrays x(0..n-1) of n elements with nondecreasing average value and 0..7 occur with instance counts within one of each other.

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A200943 Number of 0..n arrays x(0..3) of 4 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

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A200944 Number of 0..n arrays x(0..4) of 5 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

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A200945 Number of 0..n arrays x(0..5) of 6 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

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A200946 Number of 0..n arrays x(0..6) of 7 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

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