A047215 Numbers that are congruent to {0, 2} mod 5.

0, 2, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, 40, 42, 45, 47, 50, 52, 55, 57, 60, 62, 65, 67, 70, 72, 75, 77, 80, 82, 85, 87, 90, 92, 95, 97, 100, 102, 105, 107, 110, 112, 115, 117, 120, 122, 125, 127, 130, 132, 135, 137, 140, 142, 145, 147, 150, 152, 155, 157

Offset

0,2

Comments

Number of partitions of 5n into exactly 2 parts. - Colin Barker, Mar 23 2015

Numbers k such that k^2/5 + k*(k + 1)/5 = k*(2*k + 1)/5 is a nonnegative integer. - Bruno Berselli, Feb 14 2017

Links

David Lovler, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor(5*n/2).

From R. J. Mathar, Sep 23 2008: (Start)

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

a(n) = 5*n/2 + ((-1)^n-1)/4.

a(n+1) - a(n) = A010693(n+1). (End)

a(n) = 5*n - a(n-1) - 8 with a(1)=0. - Vincenzo Librandi, Aug 05 2010

a(n+1) = Sum_{k>=0} A030308(n,k)*A084215(k+1). - Philippe Deléham, Oct 17 2011

a(n) = 2*n + floor(n/2). - Arkadiusz Wesolowski, Sep 19 2012

Sum_{n>=1} (-1)^(n+1)/a(n) = log(5)/4 - sqrt(5)*log(phi)/10 + sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021

E.g.f.: (5*x*exp(x) - sinh(x))/2. - David Lovler, Aug 22 2022

Mathematica

Table[Floor[5 n/2], {n, 0, 100}] (* or *) LinearRecurrence[{1, 1, -1}, {0, 2, 5}, 101] (* Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)

Prog

(PARI) a(n)=5*n\2 \\ Charles R Greathouse IV, Oct 17 2011
(Magma) [(5*n - (n mod 2))/2: n in [1..100]]; // G. C. Greubel, Jun 23 2024
(SageMath) [int(5*n//2) for n in range(1, 101)] # G. C. Greubel, Jun 23 2024

Crossrefs

Different from A038126.

Cf. A001622, A010693, A030308, A084215

Cf. A249547 (partial sums), A010693 (1st differences).

Sequence in context: A022849 A075328 A038126 * A330067 A059536 A030193

Adjacent sequences: A047212 A047213 A047214 * A047216 A047217 A047218

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved