A133889 -id:A133889 - cp's OEIS frontend

A133879 n modulo 9 repeated 9 times.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3

Offset: 0

Hieronymus Fischer, Oct 10 2007

Periodic with length 9^2=81.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.

Cf. A133889, A133880, A133890, A133900, A133910.

Rest[Flatten[Table[Table[Table[n,{9}],{n,0,8}],{3}],1]]//Flatten (* Harvey P. Dale, Apr 15 2018 *)

a(n)=(1+floor(n/9)) mod 9.
a(n)=1+floor(n/9)-9*floor((n+9)/81).
a(n)=(((n+9) mod 81)-(n mod 9))/9.
a(n)=((n+9-(n mod 9))/9) mod 9.
G.f. g(x)=(1-x^9)(1+2x^9+3x^18+4x^27+5x^36+6x^45+7x^56+8x^63)/((1-x)(1-x^81)).
G.f. g(x)=(1-x^9)*sum{0<=k<8, (k+1)*x^(9*k)}/((1-x)(1-x^81)).
G.f. g(x)=(8x^81-9x^72+1)/((1-x)(1-x^9)(1-x^81)).

A133891 a(n) = binomial(n+p,n) mod p, where p=12.

Original entry on oeis.org

1, 1, 7, 11, 8, 8, 0, 0, 6, 2, 2, 2, 4, 4, 4, 0, 3, 3, 9, 9, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 8, 8, 5, 9, 3, 3, 8, 8, 8, 4, 10, 10, 6, 6, 0, 0, 0, 0, 3, 3, 9, 9, 0, 0, 4, 4, 4, 8, 8, 8, 0, 0, 0, 8, 5, 5, 7, 7, 4, 0, 0, 0, 6, 6, 6, 6, 0, 0, 0, 0, 3, 7, 1, 1, 8, 8, 8, 0, 0, 0, 8, 8, 8, 4, 4, 4, 9, 9, 3, 3, 0, 0, 0, 0

Offset: 0

Hieronymus Fischer, Oct 16 2007

nonn

Periodic with length 6*12^2 = 864 = A133900(12).

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636, A133910.
See A133872, A133873, A133875, A133877, A133884, A133886, A133888, A133889, A133890 for sequences with different values of p.
See A133900 for the respective periods regarding other values of p.

Table[Mod[Binomial[n+12,n],12],{n,0,110}] (* Harvey P. Dale, Oct 13 2017 *)

a(n) = binomial(n+12,12) mod 12.

A133899 Numbers m such that binomial(m+9,m) mod 9 = 0.

Original entry on oeis.org

72, 73, 74, 75, 76, 77, 78, 79, 80, 153, 154, 155, 156, 157, 158, 159, 160, 161, 234, 235, 236, 237, 238, 239, 240, 241, 242, 315, 316, 317, 318, 319, 320, 321, 322, 323, 396, 397, 398, 399, 400, 401, 402, 403, 404, 477, 478, 479, 480, 481, 482, 483, 484, 485

Offset: 0

Hieronymus Fischer, Oct 20 2007

nonn

Also numbers m such that floor(1+(m/9)) mod 9 = 0.

Partial sums of the sequence 72,1,1,1,1,1,1,1,1,73,1,1,1,1,1,1,1,1,73, ... which has period 9.

Cf. A000040, A133620, A133621, A133623, A133630, A133635.

Cf. A133879, A133889, A133890, A133900, A133910.

Select[Range[500],Divisible[Binomial[#+9,#],9]&] (* Harvey P. Dale, Apr 03 2011 *)

a(n)=9n+72-8*(n mod 9).
G.f.: g(x)=(72+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9)/((1-x^9)(1-x)).
G.f.: g(x)=(72-71x-x^10) /((1-x^9)(1-x)^2).

cp's OEIS Frontend

A133879 n modulo 9 repeated 9 times.

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A133891 a(n) = binomial(n+p,n) mod p, where p=12.

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A133899 Numbers m such that binomial(m+9,m) mod 9 = 0.

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