A126528 -id:A126528 - cp's OEIS frontend

A254599 Numbers of words on alphabet {0,1,...,9} with no subwords ii, for i from {0,1}.

1, 10, 98, 962, 9442, 92674, 909602, 8927810, 87627106, 860066434, 8441614754, 82855064258, 813228496354, 7981896981250, 78342900802082, 768941283068738, 7547214754035298, 74076463050867586, 727065885490090658, 7136204673817756610, 70042369148280534754

Offset: 0

Milan Janjic, Feb 02 2015

a(n) is the number of sequences over {0,1,...,9} of length n such that no two consecutive terms have distance 9. - David Nacin, May 31 2017

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,8).

Cf. A015584, A055099, A126473, A126501, A126528.

[n le 1 select 10^n else 9*Self(n)+8*Self(n-1): n in [0..20]]; // Bruno Berselli, Feb 02 2015

RecurrenceTable[{a[0] == 1, a[1] == 10, a[n] == 9 a[n - 1] + 8 a[n - 2]}, a[n], {n, 0, 20}] (* Bruno Berselli, Feb 02 2015 *)

Vec((1 + x)/(1 - 9*x - 8*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017

a(n) = 9*a(n-1) + 8*a(n-2) with n>1, a(0) = 1, a(1) = 10.
G.f.: (1 + x)/(1 - 9*x - 8*x^2). - Bruno Berselli, Feb 02 2015
a(n) = (2^(-1-n)*((9-r)^n*(-11+r) + (9+r)^n*(11+r))) / r, where r=sqrt(113). - Colin Barker, Jan 22 2017

A254659 Numbers of words on alphabet {0,1,...,8} with no subwords ii, where i is from {0,1,2,3}.

Original entry on oeis.org

1, 9, 77, 661, 5673, 48689, 417877, 3586461, 30781073, 264180889, 2267352477, 19459724261, 167014556473, 1433415073089, 12302393367077, 105586222302061, 906201745251873, 7777545073525289, 66751369314461677, 572898679883319861, 4916946285638867273

Offset: 0

Milan Janjic, Feb 04 2015

a(n) is the number of nonary sequences of length n such that no two consecutive terms have distance 7. - David Nacin, May 31 2017

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,5).

Cf. A015575, A055099, A126473, A126501, A126528, A254598, A254602.

[n le 1 select 9^n else 8*Self(n)+5*Self(n-1): n in [0..20]];

RecurrenceTable[{a[0] == 1, a[1] == 9, a[n] == 8 a[n - 1] + 5 a[n - 2]}, a[n], {n, 0, 20}]

Vec((1 + x)/(1 - 8*x -5*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017

G.f.: (1 + x)/(1 - 8*x - 5*x^2).
a(n) = 8*a(n-1) + 5*a(n-2) with n>1, a(0) = 1, a(1) = 9.
a(n) = ((4-r)^n*(-5+r) + (4+r)^n*(5+r)) / (2*r), where r=sqrt(21). - Colin Barker, Jan 22 2017

A254662 Numbers of words on alphabet {0,1,...,7} with no subwords ii, where i is from {0,1,...,4}.

Original entry on oeis.org

1, 8, 59, 437, 3236, 23963, 177449, 1314032, 9730571, 72056093, 533584364, 3951258827, 29259564881, 216670730648, 1604473809179, 11881328856197, 87982723420916, 651523050515003, 4824609523867769, 35726835818619392, 264561679301939051, 1959112262569431533

Offset: 0

Milan Janjic, Feb 04 2015

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,3).

Cf. A015559, A055099, A126473, A126501, A126528, A254598, A254602.

[n le 1 select 8^n else 7*Self(n)+3*Self(n-1): n in [0..20]];

RecurrenceTable[{a[0] == 1, a[1] == 8, a[n] == 7 a[n - 1] + 3 a[n - 2]}, a[n], {n, 0, 20}]

Vec((1+x)/(1-7*x-3*x^2) + O(x^30)) \\ Colin Barker, Sep 08 2016

G.f.: (1 + x)/(1 - 7*x -3*x^2).
a(n) = 7*a(n-1) + 3*a(n-2) with n>1, a(0) = 1, a(1) = 8.
a(n) = (2^(-1-n) * ((7-sqrt(61))^n * (-9+sqrt(61)) + (7+sqrt(61))^n * (9+sqrt(61)))) / sqrt(61). - Colin Barker, Sep 08 2016

cp's OEIS Frontend

A254599 Numbers of words on alphabet {0,1,...,9} with no subwords ii, for i from {0,1}.

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A254659 Numbers of words on alphabet {0,1,...,8} with no subwords ii, where i is from {0,1,2,3}.

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A254662 Numbers of words on alphabet {0,1,...,7} with no subwords ii, where i is from {0,1,...,4}.

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Mathematica

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