cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A126396 Number of base 9 n-digit numbers with adjacent digits differing by two or less.

Original entry on oeis.org

1, 9, 39, 175, 793, 3611, 16475, 75229, 343633, 1569883, 7172423, 32769925, 149723361, 684077955, 3125520983, 14280373781, 65246447425, 298108406323, 1362045450407, 6223131628517, 28433241805745, 129910355608771
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

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

Crossrefs

Cf. Base 9 differing by one or less A126363.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 + 3*x - 10*x^2 - 6*x^3 + 6*x^4 + 2*x^5) / (1 - 6*x + 5*x^2 + 8*x^3 - 4*x^4 - 2*x^5).
a(n) = 6*a(n-1) - 5*a(n-2) - 8*a(n-3) + 4*a(n-4) + 2*a(n-5) for n>5.
(End)

A126477 Number of base 9 n-digit numbers with adjacent digits differing by three or less.

Original entry on oeis.org

1, 9, 51, 301, 1787, 10619, 63111, 375091, 2229307, 13249619, 78747531, 468026571, 2781660187, 16532466059, 98258743211, 583989138891, 3470869901227, 20628701920939, 122604233247851, 728683659684651
Offset: 0

Views

Author

R. H. Hardin, Dec 27 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+7^(n-1) for base>=3n-2; a(base,n)=a(base-1,n)+7^(n-1)-2 when base=3n-3.

Crossrefs

Cf. Base 9 differing by two or less A126396, one or less A126363.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 + 2*x - 6*x^2 + 2*x^4) / ((1 - x)*(1 - 6*x + 2*x^3)).
a(n) = 7*a(n-1) - 6*a(n-2) - 2*a(n-3) + 2*a(n-4) for n>4.
(End)

A126504 Number of base 9 n-digit numbers with adjacent digits differing by four or less.

Original entry on oeis.org

1, 9, 61, 429, 3011, 21141, 148433, 1042167, 7317185, 51374875, 360709449, 2532586341, 17781606753, 124846894103, 876565722303, 6154478019155, 43211363078111, 303392406838867, 2130156189729353, 14956094122197975
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[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.

Crossrefs

Cf. Base 9 differing by three or less A126477, two or less A126396, one or less A126363.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 - x)*(1 + 3*x - x^3) / (1 - 7*x - x^2 + 6*x^3 - x^5).
a(n) = 7*a(n-1) + a(n-2) - 6*a(n-3) + a(n-5) for n>5.
(End)

A126530 Number of base 9 n-digit numbers with adjacent digits differing by five or less.

Original entry on oeis.org

1, 9, 69, 541, 4231, 33101, 258953, 2025831, 15848391, 123984439, 969949627, 7588067405, 59362636295, 464403174075, 3633098554089, 28422297349753, 222352070721709, 1739494972761653, 13608340819322255, 106460175369651261
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[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.

Crossrefs

Cf. Base 9 differing by four or less A126504, three or less A126477, two or less A126396, one or less A126363.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)
G.f.: (1 + 2*x - x^2 - x^3) / ((1 + x)*(1 - 8*x + x^2 + 3*x^3)).
a(n) = 7*a(n-1) + 7*a(n-2) - 4*a(n-3) - 3*a(n-4) for n>3.
(End)
Showing 1-4 of 4 results.

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