A047355 Numbers that are congruent to {0, 3} mod 7.

0, 3, 7, 10, 14, 17, 21, 24, 28, 31, 35, 38, 42, 45, 49, 52, 56, 59, 63, 66, 70, 73, 77, 80, 84, 87, 91, 94, 98, 101, 105, 108, 112, 115, 119, 122, 126, 129, 133, 136, 140, 143, 147, 150, 154, 157, 161, 164, 168, 171, 175, 178, 182, 185, 189, 192, 196, 199, 203

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers k such that k^2/7 + k*(k + 1)/7 = k*(2*k + 1)/7 is a nonnegative integer. - Bruno Berselli, Feb 14 2017

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A030123, A010702 (first differences).

Cf. A030308, A125176.

Programs

Haskell

a047355 n = a047355_list !! (n-1)
a047355_list = scanl (+) 0 a010702_list -- Reinhard Zumkeller, Jul 05 2012

Maple

A047355:=n->(14*n - (-1)^n - 15)/4; seq(A047355(n), n=1..100); # Wesley Ivan Hurt, Jan 30 2014

Mathematica

Table[(14n - (-1)^n - 15)/4, {n, 100}] (* Wesley Ivan Hurt, Jan 30 2014 *)

PARI

a(n)=n\2*7 - 4 + n%2*4 \\ Charles R Greathouse IV, Aug 01 2016

Formula

a(n) = a(n-2) + 7 = a(n-1) + a(n-2) - a(n-3). - Henry Bottomley, Jan 19 2001

From Bruno Berselli, Sep 12 2011: (Start)

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

a(n) = (14*n - (-1)^n - 15)/4. (End)

a(n+1) = Sum_{k>=0} A030308(n,k)*A125176(k+2). - Philippe Deléham, Oct 17 2011

a(n) = 2*n - 2 + floor((3*n - 3)/2). - Wesley Ivan Hurt, Jan 30 2014

E.g.f.: 4 + ((14*x - 15)*exp(x) - exp(-x))/4. - David Lovler, Aug 31 2022