A160529 - OEIS

%I #26 Feb 02 2023 20:41:56

%S 1,5,6,25,26,30,31,50,51,55,56,75,76,80,81,100,101,105,106,125,126,

%T 130,131,150,151,155,156,175,176,180,181,200,201,205,206,225,226,230,

%U 231,250,251,255,256,275,276,280,281,300,301,305,306,325,326,330,331,350

%N a(1) = 1; for n>1, a(n) = a(n-1) + d1 + d2 where d1 = 4 if n is even. d1 = 1 if n is odd, d2 = 15 if n mod 4 = 0, d2 = 0 if n mod 4 != 0.

%H Colin Barker, <a href="/A160529/b160529.txt">Table of n, a(n) for n = 1..1000</a>

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

%F From _Hagen von Eitzen_, May 17 2009: (Start)

%F For n>=0, a(4n+1) = 1+25n, a(4n+2) = 5+25n, a(4n+3) = 6+25n, a(4n+4) = 25+25n.

%F a(n) = 25*floor(n/4) + [0,1,5,6](n mod 4).

%F (End)

%F a(n) = a(n-1)+a(n-4)-a(n-5). G.f.: x*(1+4*x+x^2+19*x^3)/((1+x)*(x^2+1)*(x-1)^2). a(n)=-101/8+21*(-1)^n/8+15*A057077(n)/4+25*(n+1)/4. - _R. J. Mathar_, May 17 2009

%F G.f.: x*(1+4*x+x^2+19*x^3) / ((1-x^4)*(1-x)). - _Franklin T. Adams-Watters_, Jul 10 2009

%F a(n) = (-1 - 21*(-1)^n + (15-i*15)*(-i)^n + (15+15*i)*i^n + 50*n)/8 where i=sqrt(-1). - _Colin Barker_, Oct 16 2015

%t LinearRecurrence[{1,0,0,1,-1},{1,5,6,25,26},60] (* _Harvey P. Dale_, Aug 15 2011 *)

%o (C)

%o #include <stdio.h>

%o int main()

%o {

%o     int n, d1, d2; int a[101]; a[1] = 1;

%o     printf ("%d, ", a[1]);

%o     for (n=2; n<101; n++)

%o     {

%o         if (n % 2==0) d1 =4;

%o         else d1 = 1;

%o         if (n%4==0) d2 = 15;

%o         else d2=0;

%o         a[n] = a[n-1] + d1 + d2;

%o         printf ("%d, ", a[n]);

%o     }

%o     printf("\n");

%o     return 0;

%o }

%o (PARI) a(n) = (-1 - 21*(-1)^n + (15-I*15)*(-I)^n + (15+15*I)*I^n + 50*n)/8 \\ _Colin Barker_, Oct 16 2015

%o (PARI) Vec(x*(1+4*x+x^2+19*x^3)/((1-x^4)*(1-x)) + O(x^100)) \\ _Colin Barker_, Oct 16 2015

%o (Python)

%o def A160529(n): return 25*(n>>2)+(0,1,5,6)[n&3] # _Chai Wah Wu_, Feb 02 2023

%K nonn,easy

%O 1,2

%A Krishnan (krishnanrk2000(AT)yahoo.com), May 17 2009

%E Edited by _N. J. A. Sloane_, May 17 2009

%E Extended by _R. J. Mathar_, May 17 2009