A200251 -id:A200251 - cp's OEIS frontend

A200252 Number of 0..n arrays x(0..2) of 3 elements with each no smaller than the sum of its previous elements modulo (n+1).

5, 12, 26, 45, 75, 112, 164, 225, 305, 396, 510, 637, 791, 960, 1160, 1377, 1629, 1900, 2210, 2541, 2915, 3312, 3756, 4225, 4745, 5292, 5894, 6525, 7215, 7936, 8720, 9537, 10421, 11340, 12330, 13357, 14459, 15600, 16820, 18081, 19425, 20812, 22286, 23805

Offset: 1

R. H. Hardin, Nov 15 2011

Row 3 of A200251.

a(n) = A199771(n+1). - Reinhard Zumkeller, Nov 23 2011

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

R. H. Hardin, Table of n, a(n) for n = 1..210
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
From Colin Barker, Feb 19 2018: (Start)
G.f.: x*(5 + 2*x - 3*x^2 + x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).
a(n) = (n^3 + 5*n^2 + 8*n + 4) / 4 for n even.
a(n) = (n^3 + 5*n^2 + 9*n + 5) / 4 for n odd.
(End)

A200253 Number of 0..n arrays x(0..3) of 4 elements with each no smaller than the sum of its previous elements modulo (n+1).

Original entry on oeis.org

8, 24, 69, 135, 267, 448, 750, 1125, 1690, 2376, 3339, 4459, 5957, 7680, 9900, 12393, 15516, 19000, 23265, 27951, 33583, 39744, 47034, 54925, 64142, 74088, 85575, 97875, 111945, 126976, 144024, 162129, 182512, 204120, 228285, 253783, 282131, 312000

Offset: 1

R. H. Hardin, Nov 15 2011

nonn

Row 4 of A200251.

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

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

Cf. A200251.

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 3*a(n-4) - 4*a(n-5) + 4*a(n-7) - 3*a(n-8) + 2*a(n-9) - 2*a(n-11) + a(n-12).

Empirical g.f.: x*(8 + 8*x + 21*x^2 + 13*x^3 + 21*x^4 + 12*x^5 + 13*x^6 - 2*x^7 + 3*x^8 - 2*x^10 + x^11) / ((1 - x)^5*(1 + x)^3*(1 + x^2)^2). - Colin Barker, Feb 23 2018

A200254 Number of 0..n arrays x(0..4) of 5 elements with each no smaller than the sum of its previous elements modulo (n+1).

Original entry on oeis.org

13, 48, 181, 405, 951, 1792, 3434, 5625, 9365, 14256, 21855, 31213, 44863, 61440, 84500, 111537, 147789, 190000, 244905, 307461, 386903, 476928, 588990, 714025, 867061, 1037232, 1242451, 1468125, 1736895, 2031616, 2378792, 2756193, 3196493

Offset: 1

R. H. Hardin Nov 15 2011

nonn

Row 5 of A200251

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

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

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-7) +a(n-8) -4*a(n-9) +4*a(n-11) -4*a(n-12) +4*a(n-13) -4*a(n-15) +a(n-16) +2*a(n-17) -2*a(n-19) +2*a(n-20) -2*a(n-21) +2*a(n-23) -a(n-24)

A200249 Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo 6.

Original entry on oeis.org

6, 21, 75, 267, 951, 3387, 12063, 42963, 153015, 544971, 1940943, 6912771, 24620199, 87686139, 312298815, 1112268723, 3961403799, 14108748843, 50249054127, 178964660067, 637392088455, 2270105585499, 8085100933407, 28795513971219

Offset: 1

R. H. Hardin, Nov 15 2011

nonn

Column 5 of A200251.

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

R. H. Hardin, Table of n, a(n) for n = 1..136

Cf. A200251.

Empirical: a(n) = 3*a(n-1) +2*a(n-2).
Conjectures from Colin Barker, May 20 2018: (Start)
G.f.: 3*x*(2 + x) / (1 - 3*x - 2*x^2).
a(n) = (3*2^(-2-n)*((3-sqrt(17))^n*(-5+sqrt(17)) + (3+sqrt(17))^n*(5+sqrt(17)))) / sqrt(17).
(End)

A200250 Number of 0..7 arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo 8.

Original entry on oeis.org

8, 36, 164, 750, 3434, 15724, 71970, 329455, 1508139, 6903702, 31602661, 144665637, 662227235, 3031438038, 13876832881, 63523149100, 290786125630, 1331114279973, 6093362338144, 27893220846536, 127685131134366, 584496598744029

Offset: 1

R. H. Hardin, Nov 15 2011

nonn

Column 7 of A200251.

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

R. H. Hardin, Table of n, a(n) for n = 1..134

Cf. A200251.

Empirical: a(n) = a(n-1) +9*a(n-2) +24*a(n-3) +36*a(n-4) +35*a(n-5) +21*a(n-6) +7*a(n-7) +a(n-8).

Empirical g.f.: x*(2 + x)*(2 + 2*x + x^2)*(2 + 4*x + 6*x^2 + 4*x^3 + x^4) / (1 - x - 9*x^2 - 24*x^3 - 36*x^4 - 35*x^5 - 21*x^6 - 7*x^7 - x^8). - Colin Barker, May 20 2018

A200255 Number of 0..n arrays x(0..5) of 6 elements with each no smaller than the sum of its previous elements modulo (n+1).

Original entry on oeis.org

21, 96, 476, 1215, 3387, 7168, 15724, 28125, 51895, 85536, 143052, 218491, 337869, 491520, 721208, 1003833, 1407681, 1900000, 2578060, 3382071, 4457431, 5723136, 7375716, 9282325, 11720787, 14521248, 18038972, 22021875, 26948985, 32505856

Offset: 1

R. H. Hardin Nov 15 2011

nonn

Row 6 of A200251

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

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

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-7) -2*a(n-9) +2*a(n-11) -2*a(n-12) +2*a(n-13) -2*a(n-15) +3*a(n-16) -4*a(n-17) +4*a(n-19) -4*a(n-20) +4*a(n-21) -4*a(n-23) +4*a(n-25) -4*a(n-27) +4*a(n-28) -4*a(n-29) +4*a(n-31) -3*a(n-32) +2*a(n-33) -2*a(n-35) +2*a(n-36) -2*a(n-37) +2*a(n-39) -2*a(n-41) +2*a(n-43) -2*a(n-44) +2*a(n-45) -2*a(n-47) +a(n-48)

A200256 Number of 0..n arrays x(0..6) of 7 elements with each no smaller than the sum of its previous elements modulo (n+1).

Original entry on oeis.org

34, 192, 1252, 3645, 12063, 28672, 71970, 140625, 287570, 513216, 936348, 1529437, 2544535, 3932160, 6155908, 9034497, 13408074, 19000000, 27138660, 37202781, 51353159, 68677632, 92363430, 120670225, 158439658, 203297472, 261905308

Offset: 1

R. H. Hardin Nov 15 2011

nonn

Row 7 of A200251

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

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

Empirical: a(n) = 2*a(n-1) -2*a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-7) -2*a(n-9) +2*a(n-11) -2*a(n-12) +2*a(n-13) -2*a(n-15) +2*a(n-16) -2*a(n-17) +2*a(n-19) -2*a(n-20) +2*a(n-21) -2*a(n-23) +2*a(n-25) -2*a(n-27) +2*a(n-28) -2*a(n-29) +2*a(n-31) +a(n-32) -4*a(n-33) +4*a(n-35) -4*a(n-36) +4*a(n-37) -4*a(n-39) +4*a(n-41) -4*a(n-43) +4*a(n-44) -4*a(n-45) +4*a(n-47) -4*a(n-48) +4*a(n-49) -4*a(n-51) +4*a(n-52) -4*a(n-53) +4*a(n-55) -4*a(n-57) +4*a(n-59) -4*a(n-60) +4*a(n-61) -4*a(n-63) +a(n-64) +2*a(n-65) -2*a(n-67) +2*a(n-68) -2*a(n-69) +2*a(n-71) -2*a(n-73) +2*a(n-75) -2*a(n-76) +2*a(n-77) -2*a(n-79) +2*a(n-80) -2*a(n-81) +2*a(n-83) -2*a(n-84) +2*a(n-85) -2*a(n-87) +2*a(n-89) -2*a(n-91) +2*a(n-92) -2*a(n-93) +2*a(n-95) -a(n-96)

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A200252 Number of 0..n arrays x(0..2) of 3 elements with each no smaller than the sum of its previous elements modulo (n+1).

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A200253 Number of 0..n arrays x(0..3) of 4 elements with each no smaller than the sum of its previous elements modulo (n+1).

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A200254 Number of 0..n arrays x(0..4) of 5 elements with each no smaller than the sum of its previous elements modulo (n+1).

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A200249 Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo 6.

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A200250 Number of 0..7 arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo 8.

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A200255 Number of 0..n arrays x(0..5) of 6 elements with each no smaller than the sum of its previous elements modulo (n+1).

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A200256 Number of 0..n arrays x(0..6) of 7 elements with each no smaller than the sum of its previous elements modulo (n+1).

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