A269640 -id:A269640 - cp's OEIS frontend

A269634 Number of length-n 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

2, 9, 60, 567, 6876, 101999, 1789528, 36254755, 833022466, 21405491763, 608269658548, 18940014187981, 641288235101528, 23458631849042641, 921973961506659528, 38744802632600163683, 1733648542829648188818

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

Diagonal of A269640.

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

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

Cf. A269640.

A269635 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

4, 16, 60, 221, 796, 2828, 9928, 34537, 119236, 409098, 1396288, 4744671, 16062116, 54199810, 182382428, 612236251, 2050883956, 6857469364, 22892085300, 76311433969, 254067536796, 844941922160, 2807225267056, 9318543171653

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

			Some solutions for n=9:
..2. .1. .2. .1. .2. .0. .2. .1. .1. .1. .1. .3. .3. .0. .0. .2
..0. .2. .3. .3. .2. .1. .0. .3. .3. .2. .3. .0. .1. .2. .2. .0
..3. .0. .0. .0. .1. .3. .0. .2. .2. .2. .0. .1. .3. .0. .1. .3
..1. .3. .2. .1. .0. .2. .1. .3. .1. .0. .3. .1. .0. .1. .3. .1
..0. .0. .2. .1. .3. .0. .0. .2. .3. .2. .1. .0. .3. .2. .0. .2
..1. .1. .0. .2. .2. .2. .2. .0. .2. .3. .2. .3. .0. .1. .3. .3
..3. .3. .3. .0. .3. .3. .2. .1. .0. .1. .0. .2. .0. .2. .2. .1
..0. .3. .2. .1. .1. .2. .1. .2. .1. .3. .2. .0. .2. .3. .0. .0
..0. .0. .0. .0. .2. .0. .3. .1. .0. .1. .2. .2. .0. .2. .3. .2

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

Column 3 of A269640.

Empirical: a(n) = 9*a(n-1) - 21*a(n-2) - 19*a(n-3) + 93*a(n-4) + 27*a(n-5) - 133*a(n-6) - 87*a(n-7).

Empirical g.f.: x*(4 - 20*x + 93*x^3 - x^4 - 151*x^5 - 89*x^6) / ((1 - 3*x)*(1 - 6*x + 3*x^2 + 28*x^3 - 9*x^4 - 54*x^5 - 29*x^6)). - Colin Barker, Jan 25 2019

A269636 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

5, 25, 120, 567, 2637, 12125, 55225, 249600, 1120868, 5006144, 22255415, 98544130, 434827380, 1912861067, 8392454605, 36733957588, 160447861687, 699496998228, 3044446874255, 13230474539089, 57418454111103, 248881927670961

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

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

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

Column 4 of A269640.

Empirical: a(n) = 13*a(n-1) - 51*a(n-2) + 15*a(n-3) + 240*a(n-4) - 96*a(n-5) - 509*a(n-6) - 268*a(n-7).

Empirical g.f.: x*(5 - 40*x + 50*x^2 + 207*x^3 - 189*x^4 - 559*x^5 - 273*x^6) / ((1 - 4*x)*(1 - 9*x + 15*x^2 + 45*x^3 - 60*x^4 - 144*x^5 - 67*x^6)). - Colin Barker, Jan 25 2019

A269637 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

6, 36, 210, 1209, 6876, 38738, 216528, 1202353, 6639294, 36486190, 199677806, 1088813760, 5918190122, 32077034918, 173421804818, 935474530883, 5035906367464, 27059901888584, 145161762258568, 777537033208493

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

Column 5 of A269640.

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

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

Cf. A269640.

Empirical: a(n) = 29*a(n-1) -330*a(n-2) +1730*a(n-3) -2815*a(n-4) -9981*a(n-5) +36088*a(n-6) +31192*a(n-7) -161403*a(n-8) -158561*a(n-9) +291970*a(n-10)

A269638 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

7, 49, 336, 2279, 15307, 101999, 675151, 4443665, 29104549, 189818232, 1233390075, 7987992466, 51583193592, 332235953819, 2134851774996, 13688959603199, 87607353750867, 559696980939927, 3570042462583517, 22738396298175560

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

Column 6 of A269640.

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

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

Cf. A269640.

Empirical: a(n) = 42*a(n-1) -735*a(n-2) +6748*a(n-3) -32319*a(n-4) +53130*a(n-5) +172660*a(n-6) -705975*a(n-7) -416955*a(n-8) +3381035*a(n-9) +2527266*a(n-10) -7375032*a(n-11) -13093923*a(n-12) -7922412*a(n-13) -1718604*a(n-14)

A269639 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

8, 64, 504, 3933, 30444, 234080, 1789528, 13613507, 103118640, 778158768, 5852649288, 43888314093, 328240366020, 2449045039552, 18233174801384, 135479775215950, 1004866303875264, 7440970750295140, 55016954785772120

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

Column 7 of A269640.

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

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

Cf. A269640.

Empirical: a(n) = 56*a(n-1) -1344*a(n-2) +17752*a(n-3) -135716*a(n-4) +545496*a(n-5) -463786*a(n-6) -4675564*a(n-7) +12243456*a(n-8) +21822328*a(n-9) -72836660*a(n-10) -123804240*a(n-11) +151424498*a(n-12) +520495760*a(n-13) +515921322*a(n-14) +232811740*a(n-15) +41061559*a(n-16)

A269641 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

9, 63, 221, 567, 1209, 2279, 3933, 6351, 9737, 14319, 20349, 28103, 37881, 50007, 64829, 82719, 104073, 129311, 158877, 193239, 232889, 278343, 330141, 388847, 455049, 529359, 612413, 704871, 807417, 920759, 1045629, 1182783, 1333001

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

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

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

Row 4 of A269640.

Empirical: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n - 1.
Conjectures from Colin Barker, Jan 25 2019: (Start)
G.f.: x*(3 - x)*(3 + 7*x + x^2 + x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A269642 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

12, 159, 796, 2637, 6876, 15307, 30444, 55641, 95212, 154551, 240252, 360229, 523836, 741987, 1027276, 1394097, 1858764, 2439631, 3157212, 4034301, 5096092, 6370299, 7887276, 9680137, 11784876, 14240487, 17089084, 20376021, 24150012

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

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

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

Row 5 of A269640.

Empirical: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 5*n + 1.
Conjectures from Colin Barker, Jan 25 2019: (Start)
G.f.: x*(12 + 87*x + 22*x^2 + 6*x^3 - 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A269643 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

16, 396, 2828, 12125, 38738, 101999, 234080, 484673, 926390, 1660883, 2825684, 4601765, 7221818, 10979255, 16237928, 23442569, 33129950, 45940763, 62632220, 84091373, 111349154, 145595135, 188193008, 240696785, 304867718, 382691939

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

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

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

Row 6 of A269640.

Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 12*n^2 + 9*n - 7 for n>2.
Conjectures from Colin Barker, Jan 25 2019: (Start)
G.f.: x*(16 + 284*x + 392*x^2 + 85*x^3 - 49*x^4 + 2*x^5 - 14*x^6 + 5*x^7 - x^8) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.
(End)

A269644 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

Original entry on oeis.org

20, 969, 9928, 55225, 216528, 675151, 1789528, 4200933, 8974480, 17780443, 33120936, 58606993, 99291088, 162060135, 256094008, 393394621, 589390608, 863622643, 1240514440, 1750234473, 2429653456, 3323402623, 4485037848

Offset: 1

R. H. Hardin, Mar 02 2016

nonn

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

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

Row 7 of A269640.

Empirical: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 22*n^3 + 28*n^2 - 37*n + 13 for n>2.
Conjectures from Colin Barker, Jan 25 2019: (Start)
G.f.: x*(20 + 809*x + 2736*x^2 + 1813*x^3 - 152*x^4 - 31*x^5 - 240*x^6 + 123*x^7 - 44*x^8 + 6*x^9)  / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>10.
(End)

cp's OEIS Frontend

A269634 Number of length-n 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269635 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269636 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269637 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269638 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269639 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269641 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269642 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269643 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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A269644 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.

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