A257847 a(n) = floor(n/7) * (n mod 7).

0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 2, 4, 6, 8, 10, 12, 0, 3, 6, 9, 12, 15, 18, 0, 4, 8, 12, 16, 20, 24, 0, 5, 10, 15, 20, 25, 30, 0, 6, 12, 18, 24, 30, 36, 0, 7, 14, 21, 28, 35, 42, 0, 8, 16, 24, 32, 40, 48, 0, 9, 18, 27, 36, 45, 54, 0, 10, 20

Offset

0,10

Comments

Equivalently, write n in base 7, multiply the last digit by the number with its last digit removed.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,2,0,0,0,0,0,0,-1).

Formula

a(n) = 2*a(n-7)-a(n-14). - Colin Barker, May 11 2015

G.f.: x^8*(6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^6+x^5+x^4+x^3+x^2+x+1)^2). - Colin Barker, May 11 2015

Mathematica

Table[Floor[n/7]Mod[n, 7], {n, 0, 80}] (* Harvey P. Dale, Nov 12 2022 *)

Prog

(PARI) a(n, b=7)=(n=divrem(n, b))[1]*n[2]
(PARI) concat([0, 0, 0, 0, 0, 0, 0, 0], Vec(x^8*(6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^6+x^5+x^4+x^3+x^2+x+1)^2) + O(x^100))) \\ Colin Barker, May 11 2015

Crossrefs

Cf. A194757.

Cf. A142150 (the base 2 analog), A115273, A257844 - A257850.

Sequence in context: A309958 A055400 A367842 * A194757 A070553 A204453

Adjacent sequences: A257844 A257845 A257846 * A257848 A257849 A257850

Keyword

nonn,base,easy

Author

M. F. Hasler, May 10 2015

Status

approved