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

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

Author

Hieronymus Fischer, Oct 20 2007

Keywords

• nonn
• easy

Comments

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.

Links

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

Crossrefs

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

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

Programs

Mathematica

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 *)

PARI

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

Formula

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).