reviewed

approved

proposed

reviewed

editing

proposed

Numbers == 1, 3, 7, 13 modulo 20. - Ralf Stephan, May 15 2007

a(n) = a(n-1) + a(n-4) - a(n-5), with a(0)=1, a(1)=3, a(2)=7, a(3)=13, a(4)=21, a(n) = a(n-1)+a(n-4)-a(n-5). - Harvey P. Dale, Apr 09 2012

G.f.: (71+2*x^+4*x^2+6*x^3+47*x^2+2*x+4)/((1)/((-x-1)^2*(1+x^3+x^2+x+1^3)). - Harvey P. Dale, Apr 09 2012

a(n) = (5*n - (3/2+-(-1)^n)/2 +(- i)^n + (-i)^n+5*n) , where i=sqrt(-1). - Colin Barker, Oct 16 2015

E.g.f.: (5*x-1)*cosh(x) + (5*x-2)*sinh(x) + 2*cos(x). - G. C. Greubel, Jun 30 2022

digits=200 f[n_]:= f[n]= If[n==0, 1, f[n-1]+Mod[2*n-1, 8]+1 f[0]=1; a=Table[f[n], {n, 1, digits0, 100}]

(PARI) a(n) = (5*n-3/2+(-1)^n/2+(-I)^n+I^n+5*n) \\ Colin Barker, Oct 16 2015

(Magma) [n mod 2 eq 0 select Round(5*n-1+2*(-1)^(n/2)) else Round(5*n-2): n in [0..100]]; // G. C. Greubel, Jun 30 2022

(SageMath) [5*n-1 -(n%2) +2*i^n*((n+1)%2) for n in (0..60)] # G. C. Greubel, Jun 30 2022

approved

editing

editing

approved

a(n) = a(n-1) + Mod[(2*n - 1,) mod 8] + 1 with a(0)=1.

a(n) = (-3/2+(-1)^n/2+(-Ii)^n+Ii^n+5*n) where Ii=sqrt(-1). - Colin Barker, Oct 16 2015

approved

editing

proposed

approved

editing

proposed

a(n) = a(n-1) + Mod[2*n-1,8] + 1; with a(0)=1.

Colin Barker, <a href="/A100531/b100531.txt">Table of n, a(n) for n = 0..1000</a>

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1).

a(0)=1, a(1)=3, a(2)=7, a(3)=13, a(4)=21, a(n) = a(n-1)+a(n-4)-a(n-5) [From . - _Harvey P. Dale, _, Apr 09 2012]

G.f.: (7*x^4+6*x^3+4*x^2+2*x+1)/((x-1)^2*(x^3+x^2+x+1)) [From . - _Harvey P. Dale, _, Apr 09 2012]

a(n) = (-3/2+(-1)^n/2+(-I)^n+I^n+5*n) where I=sqrt(-1). - Colin Barker, Oct 16 2015

(PARI) a(n) = (-3/2+(-1)^n/2+(-I)^n+I^n+5*n) \\ Colin Barker, Oct 16 2015

(PARI) Vec((7*x^4+6*x^3+4*x^2+2*x+1)/((x-1)^2*(x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Oct 16 2015

nonn,easy

approved

editing

editing

approved