A272574 a(n) = f(9, f(8, n)), where f(k,m) = floor(m*k/(k-1)).

0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 41, 42, 45, 46, 47, 48, 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 90

Offset: 0

Author

Bruno Berselli, May 03 2016

Keywords

• nonn
• easy

Comments

Also, numbers that are congruent to {0..6} mod 9.

The initial terms coincide with those of A037475 and A039111. First disagreement is after 60 (index 48): a(49) = 63, A037475(49) = 81 and A039111(50) = 71.

Links

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

Crossrefs

Cf. A248375: f(9,n).

Cf. similar sequences with the formula f(k, f(k-1, n)): A008585 (k=3), A042948 (k=4), A047217 (k=5), A047246 (k=6), A047337 (k=7), A047602 (k=8), this sequence (k=9), A272576 (k=10).

Programs

Magma

k:=9; f:=func; [f(k,f(k-1,n)): n in [0..70]];

Maple

f := (k, m) -> floor(m*k/(k-1)):
a := n -> f(9, f(8, n)):
seq(a(n), n = 0..70); # Peter Luschny, May 03 2016

Mathematica

f[k_, m_] := Floor[m*k/(k-1)];
a[n_] := f[9, f[8, n]];
Table[a[n], {n, 0, 70}] (* Jean-François Alcover, May 09 2016 *)
CoefficientList[Series[x (1 + x + x^2 + x^3 + x^4 + x^5 + 3 x^6)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)), {x, 0, 70}], x] (* or *)
Table[(63 n - 12 - 12 Mod[n, 7] + 2 Mod[-n - 1, 7])/49, {n, 0, 70}] (* Michael De Vlieger, Dec 25 2016 *)
LinearRecurrence[{1,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,9},90] (* Harvey P. Dale, May 08 2018 *)

Sage

f = lambda k, m: floor(m*k/(k-1))
a = lambda n: f(9, f(8, n))
[a(n) for n in range(71)] # Peter Luschny, May 03 2016

Formula

G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 + 3*x^6)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

a(n) = a(n-1) + a(n-7) - a(n-8).

a(n) = (63*n - 12 - 12*(n mod 7) + 2*((-n-1) mod 7))/49. - Wesley Ivan Hurt, Dec 25 2016