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 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
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 CROSSREFS Sequence in context: A042283 A047186 A166591 * 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

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Last modified October 24 01:08 EDT 2018. Contains 316541 sequences. (Running on oeis4.)