A160529 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.

1, 5, 6, 25, 26, 30, 31, 50, 51, 55, 56, 75, 76, 80, 81, 100, 101, 105, 106, 125, 126, 130, 131, 150, 151, 155, 156, 175, 176, 180, 181, 200, 201, 205, 206, 225, 226, 230, 231, 250, 251, 255, 256, 275, 276, 280, 281, 300, 301, 305, 306, 325, 326, 330, 331, 350

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

From Hagen von Eitzen, May 17 2009: (Start)

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

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

(End)

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

G.f.: x*(1+4*x+x^2+19*x^3) / ((1-x^4)*(1-x)). - Franklin T. Adams-Watters, Jul 10 2009

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

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 5, 6, 25, 26}, 60] (* Harvey P. Dale, Aug 15 2011 *)

Prog

(C)
#include <stdio.h>
int main()
{
    int n, d1, d2; int a[101]; a[1] = 1;
    printf ("%d, ", a[1]);
    for (n=2; n<101; n++)
    {
        if (n % 2==0) d1 =4;
        else d1 = 1;
        if (n%4==0) d2 = 15;
        else d2=0;
        a[n] = a[n-1] + d1 + d2;
        printf ("%d, ", a[n]);
    }
    printf("\n");
    return 0;
}
(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
(PARI) Vec(x*(1+4*x+x^2+19*x^3)/((1-x^4)*(1-x)) + O(x^100)) \\ Colin Barker, Oct 16 2015
(Python)
def A160529(n): return 25*(n>>2)+(0, 1, 5, 6)[n&3] # Chai Wah Wu, Feb 02 2023

Crossrefs

Sequence in context: A335827 A166591 A342610 * A039572 A033042 A039594

Adjacent sequences: A160526 A160527 A160528 * A160530 A160531 A160532

Keyword

nonn,easy

Author

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

Extensions

Edited by N. J. A. Sloane, May 17 2009

Extended by R. J. Mathar, May 17 2009

Status

approved