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A160529
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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.
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1
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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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
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
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 1, -1}, {1, 5, 6, 25, 26}, 60] (* Harvey P. Dale, Aug 15 2011 *)
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Krishnan (krishnanrk2000(AT)yahoo.com), May 17 2009
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EXTENSIONS
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STATUS
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approved
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