A200763 -id:A200763 - cp's OEIS frontend

A200759 Number of 0..3 arrays x(0..n-1) of n elements with nondecreasing average value.

4, 10, 23, 51, 110, 233, 488, 1013, 2088, 4278, 8720, 17695, 35768, 72054, 144717, 289887, 579312, 1155257, 2299426, 4568935, 9064316, 17957296, 35529320, 70213565, 138607340, 273351142, 538591471, 1060310343, 2085784818, 4100099321

Offset: 1

R. H. Hardin, Nov 22 2011

nonn

Column 3 of A200763

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

R. H. Hardin, Table of n, a(n) for n = 1..174

Empirical: a(n) = 5*a(n-1) -8*a(n-2) +3*a(n-3) +3*a(n-4) -2*a(n-5) +a(n-6) -3*a(n-7) +2*a(n-8) -a(n-9) +a(n-10).

Empirical g.f.: -x*(4-10*x+5*x^2+4*x^3-3*x^4-3*x^6+x^9+2*x^7-x^8) / ( (x-1)*(x^3+x^2+x-1)*(x^6-x^5+2*x^4-x^3-2*x^2+3*x-1) ). - R. J. Mathar, Nov 22 2011

A200760 Number of 0..4 arrays x(0..n-1) of n elements with nondecreasing average value.

Original entry on oeis.org

5, 15, 42, 113, 297, 767, 1957, 4947, 12419, 31006, 77067, 190855, 471214, 1160452, 2851731, 6995305, 17133294, 41909286, 102399361, 249960246, 609662706, 1485944622, 3619527395, 8811972483, 21443566290, 52161461882, 126839318918

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Column 4 of A200763

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

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

Empirical: a(n) = 18*a(n-1) -147*a(n-2) +718*a(n-3) -2324*a(n-4) +5207*a(n-5) -8163*a(n-6) +8783*a(n-7) -5967*a(n-8) +1216*a(n-9) +4359*a(n-10) -12032*a(n-11) +21061*a(n-12) -25355*a(n-13) +19242*a(n-14) -4565*a(n-15) -10182*a(n-16) +15832*a(n-17) -9350*a(n-18) -2623*a(n-19) +9836*a(n-20) -8451*a(n-21) +2304*a(n-22) +2965*a(n-23) -4284*a(n-24) +2384*a(n-25) -124*a(n-26) -752*a(n-27) +543*a(n-28) -103*a(n-29) -133*a(n-30) +128*a(n-31) -53*a(n-32) +19*a(n-33) -12*a(n-34) +3*a(n-35) +9*a(n-36) -6*a(n-37) -a(n-38) +2*a(n-39) -a(n-41)

A200761 Number of 0..5 arrays x(0..n-1) of n elements with nondecreasing average value.

Original entry on oeis.org

6, 21, 69, 219, 679, 2070, 6235, 18608, 55148, 162532, 476857, 1393903, 4061917, 11805549, 34234268, 99079243, 286255570, 825770674, 2378862529, 6844519217, 19671211354, 56477811098, 162002541976, 464298401040, 1329640943422

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Column 5 of A200763

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

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

A200762 Number of 0..6 arrays x(0..n-1) of n elements with nondecreasing average value.

Original entry on oeis.org

7, 28, 106, 388, 1387, 4874, 16919, 58198, 198807, 675372, 2283994, 7695280, 25845198, 86568033, 289279804, 964690182, 3211220933, 10672137362, 35416362298, 117378654202, 388561273645, 1284874248757, 4244554964082

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Column 6 of A200763

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

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

A200764 Number of 0..n arrays x(0..3) of 4 elements with nondecreasing average value.

Original entry on oeis.org

5, 19, 51, 113, 219, 388, 638, 995, 1483, 2133, 2975, 4047, 5383, 7028, 9022, 11415, 14253, 17593, 21485, 25993, 31173, 37094, 43818, 51421, 59969, 69545, 80221, 92085, 105215, 119706, 135640, 153119, 172231, 193083, 215769, 240403, 267083, 295930

Offset: 1

R. H. Hardin, Nov 22 2011

nonn

a(n) is the number of integer lattice points in n*C where C is the polytope in R^4 with vertices [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 1], [0, 0, 1, 1/3], [0, 1, 1, 1], [0, 1, 1, 2/3], [0, 1, 1/2, 1], [0, 1, 1/2, 1/2], [1, 1, 1, 1], and thus is an Ehrhart quasi-polynomial. - Robert Israel, May 30 2025

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

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

Row 4 of A200763.

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).

Empirical g.f.: -x*(5+9*x+8*x^2+7*x^3+4*x^4+4*x^5-x^6-2*x^7+x^8) / ( (1+x+x^2)*(1+x)^2*(x-1)^5 ). - R. J. Mathar, Nov 22 2011

A200765 Number of 0..n arrays x(0..4) of 5 elements with nondecreasing average value.

Original entry on oeis.org

6, 32, 110, 297, 679, 1387, 2583, 4500, 7410, 11669, 17687, 25980, 37111, 51787, 70763, 94950, 125323, 163042, 209312, 265570, 333296, 414214, 510106, 623032, 755080, 908676, 1086266, 1290643, 1524638, 1791469, 2094349, 2436949, 2822922

Offset: 1

R. H. Hardin, Nov 22 2011

nonn

Row 5 of A200763

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

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

Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-4) -3*a(n-5) +3*a(n-6) +3*a(n-7) +a(n-8) -3*a(n-9) -3*a(n-10) +a(n-11) +3*a(n-12) +3*a(n-13) -3*a(n-14) -3*a(n-15) +2*a(n-17) +a(n-18) -a(n-19)

Empirical g.f.: -x*(-6 -26*x -66*x^2 -123*x^3 -180*x^4 -228*x^5 -246*x^6 -250*x^7 -240*x^8 -222*x^9 -184*x^10 -129*x^11 -69*x^12 -21*x^13 -2*x^14 -x^15 -2*x^16 -x^17+x^18) / ( (x^2+1) *(x^4+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^6 ). - R. J. Mathar, Nov 22 2011

A200766 Number of 0..n arrays x(0..5) of 6 elements with nondecreasing average value.

Original entry on oeis.org

7, 53, 233, 767, 2070, 4874, 10283, 20012, 36412, 62780, 103412, 164018, 251615, 375282, 545834, 776713, 1083692, 1485962, 2005409, 2668396, 3504549, 4548781, 5840076, 7423854, 9349952, 11676207, 14465536, 17789881, 21727318, 26366500

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Row 6 of A200763

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

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

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -2*a(n-4) -3*a(n-5) +2*a(n-6) +2*a(n-7) +4*a(n-8) -5*a(n-9) -4*a(n-10) -a(n-11) +5*a(n-12) +7*a(n-13) -5*a(n-14) -3*a(n-15) -6*a(n-16) +6*a(n-17) +4*a(n-18) +a(n-19) -a(n-20) -7*a(n-21) +2*a(n-22) -2*a(n-23) +7*a(n-24) +a(n-25) -a(n-26) -4*a(n-27) -6*a(n-28) +6*a(n-29) +3*a(n-30) +5*a(n-31) -7*a(n-32) -5*a(n-33) +a(n-34) +4*a(n-35) +5*a(n-36) -4*a(n-37) -2*a(n-38) -2*a(n-39) +3*a(n-40) +2*a(n-41) -a(n-42) -a(n-43) -a(n-44) +a(n-45)

A200767 Number of 0..n arrays x(0..6) of 7 elements with nondecreasing average value.

Original entry on oeis.org

8, 87, 488, 1957, 6235, 16919, 40437, 87914, 176767, 333702, 597390, 1023102, 1685581, 2687038, 4160030, 6277804, 9258994, 13381323, 18984366, 26491458, 36409891, 49357180, 66063593, 87404568, 114396287, 148245212, 190335373

Offset: 1

R. H. Hardin Nov 22 2011

nonn

Row 7 of A200763

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

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

cp's OEIS Frontend

A200759 Number of 0..3 arrays x(0..n-1) of n elements with nondecreasing average value.

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A200760 Number of 0..4 arrays x(0..n-1) of n elements with nondecreasing average value.

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A200761 Number of 0..5 arrays x(0..n-1) of n elements with nondecreasing average value.

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A200762 Number of 0..6 arrays x(0..n-1) of n elements with nondecreasing average value.

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A200764 Number of 0..n arrays x(0..3) of 4 elements with nondecreasing average value.

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A200765 Number of 0..n arrays x(0..4) of 5 elements with nondecreasing average value.

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A200766 Number of 0..n arrays x(0..5) of 6 elements with nondecreasing average value.

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A200767 Number of 0..n arrays x(0..6) of 7 elements with nondecreasing average value.

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