A257845 a(n) = floor(n/5) * (n mod 5).

0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 0, 2, 4, 6, 8, 0, 3, 6, 9, 12, 0, 4, 8, 12, 16, 0, 5, 10, 15, 20, 0, 6, 12, 18, 24, 0, 7, 14, 21, 28, 0, 8, 16, 24, 32, 0, 9, 18, 27, 36, 0, 10, 20, 30, 40, 0, 11, 22, 33, 44, 0, 12, 24, 36, 48, 0, 13, 26, 39, 52, 0, 14, 28, 42, 56

Offset

0,8

Comments

Equivalently, write n in base 5, 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 (0,0,0,0,2,0,0,0,0,-1).

Formula

a(n) = 2*a(n-5) - a(n-10). - Colin Barker, May 11 2015

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

Mathematica

LinearRecurrence[{0, 0, 0, 0, 2, 0, 0, 0, 0, -1}, {0, 0, 0, 0, 0, 0, 1, 2, 3, 4}, 80] (* Harvey P. Dale, Aug 15 2021 *)

Prog

(PARI) a(n, b=5)=(n=divrem(n, b))[1]*n[2]
(PARI) concat([0, 0, 0, 0, 0, 0], Vec(x^6*(1+2*x+3*x^2+4*x^3)/(1-x^5)^2 + O(x^100))) \\ Colin Barker, May 11 2015
(Magma)
A257845:= func< n | Floor(n/5)*(n mod 5) >;
[A257845(n): n in [0..40]]; // G. C. Greubel, Jan 21 2026
(SageMath)
def A257845(n): return (n//5) * (n%5)
print([A257845(n) for n in range(101)]) # G. C. Greubel, Jan 21 2026

Crossrefs

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

Sequence in context: A394562 A394758 A190886 * A162593 A279125 A011025

Adjacent sequences: A257842 A257843 A257844 * A257846 A257847 A257848

Keyword

nonn,easy

Author

M. F. Hasler, May 10 2015

Status

approved