A133878 -id:A133878 - cp's OEIS frontend

A133888 Binomial(n+8,n) mod 8.

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

Offset: 0

Hieronymus Fischer, Oct 10 2007

nonn

Periodic with length 8^2=64.

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

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

Cf. A133878, A133880, A133890, A133900, A133910.

Table[Mod[Binomial[n+8,n],8],{n,0,110}] (* Harvey P. Dale, Aug 08 2011 *)

a(n)=binomial(n+8,8) mod 8.

A133898 Numbers m such that binomial(m+8,m) mod 8 = 0.

Original entry on oeis.org

56, 57, 58, 59, 60, 61, 62, 63, 120, 121, 122, 123, 124, 125, 126, 127, 184, 185, 186, 187, 188, 189, 190, 191, 248, 249, 250, 251, 252, 253, 254, 255, 312, 313, 314, 315, 316, 317, 318, 319, 376, 377, 378, 379, 380, 381, 382, 383, 440, 441, 442, 443, 444

Offset: 0

Hieronymus Fischer, Oct 20 2007

Partial sums of the sequence 56,1,1,1,1,1,1,1,57,1,1,1,1,1,1,1,57, ... which has period 8.

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

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

Cf. A133878, A133888, A133890, A133900, A133910.

Select[Range[500],Mod[Binomial[#+8,#],8]==0&] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{56,57,58,59,60,61,62,63,120},60] (* Harvey P. Dale, Apr 07 2025 *)

a(n)=8*n+56-n%8*7 \\ Charles R Greathouse IV, Oct 13 2022

a(n)=8n+56-7*(n mod 8). [Corrected by Charles R Greathouse IV, Oct 13 2022]
G.f.: g(x)=(56+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8)/((1-x^8)(1-x)).
G.f.: g(x)=(56-55x-x^9) /((1-x^8)(1-x)^2).

cp's OEIS Frontend

A133888 Binomial(n+8,n) mod 8.

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