A126478 -id:A126478 - cp's OEIS frontend

A126505 Number of base 10 n-digit numbers with adjacent digits differing by four or less.

1, 10, 70, 510, 3720, 27142, 198034, 1444904, 10542368, 76919662, 561224422, 4094828862, 29876859864, 217988781808, 1590498774316, 11604663002012, 84670422615182, 617775842744470, 4507441679052256, 32887382581680414

Offset: 0

R. H. Hardin, Dec 28 2006

[Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.

Base 10 differing by three or less A126478, two or less A126397, one or less A126364.

Conjectures from Colin Barker, May 31 2017: (Start)
G.f.: (1 + 3*x - 3*x^2 - 4*x^3 + x^4 + x^5) / (1 - 7*x - 3*x^2 + 6*x^3 + x^4 - x^5).
a(n) = 7*a(n-1) + 3*a(n-2) - 6*a(n-3) - a(n-4) + a(n-5) for n>5.
(End)

A126531 Number of base 10 n-digit numbers with adjacent digits differing by five or less.

Original entry on oeis.org

1, 10, 80, 660, 5430, 44692, 367826, 3027314, 24915652, 205062892, 1687725824, 13890462738, 114322452324, 940906242802, 7743925534706, 63734705924048, 524554726284436, 4317234336897124, 35532064407664766, 292438978880594940

Offset: 0

R. H. Hardin, Dec 28 2006

[Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5.

Cf. Base 10 differing by four or less A126505, three or less A126478, two or less A126397, one or less A126364.

Conjectures from Colin Barker, May 31 2017: (Start)
G.f.: (1 - x)*(1 + 3*x - x^3) / ((1 + x)*(1 - 9*x + 6*x^2 + 3*x^3 - 2*x^4)).
a(n) = 8*a(n-1) + 3*a(n-2) - 9*a(n-3) - a(n-4) + 2*a(n-5) for n>4.
(End)

cp's OEIS Frontend

A126505 Number of base 10 n-digit numbers with adjacent digits differing by four or less.

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