A112569 Antidiagonal sums of square table A112564 of generalized Flavius Josephus sieves.

1, 2, 4, 9, 19, 43, 88, 207, 423, 951, 2094, 4511, 9445, 22025, 45172, 93483, 205101, 435515, 882322, 1983637, 3983429, 8659805, 17928712, 36742421, 76317521, 163095069, 331056988, 693360803, 1444266731

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Index entries for sequences related to the Josephus Problem

Prog

(C++) #include <iostream> #include <limits.h> using namespace std ; int A112564(const unsigned long long n, const unsigned long long k) { unsigned long long A=k ; unsigned long long B=0 ; unsigned long long C=0 ; if( n==0 || k == 0) return 1; else { while(A != B) { C++ ; if ( C % n == 0) C++ ; B=A ; A= A*(C+1)/C ; if ( A > ULLONG_MAX/(C+1) ) exit(0) ; } return 1+A ; } } unsigned long long A112569(const int d) { unsigned long long resul =0 ; for(int k=0 ; k <=d ; k++) resul += A112564(d-k, k) ; return resul ; } int main(int argc, char *argv[]) { for(int n=0; n < 40 ; n++) cout << A112569(n) << endl ; } - R. J. Mathar, Sep 26 2006
(PARI) A112564(n, k)= {my(A=k, B=0, C=0); if(n==0 || k==0, 1, until(A==B, C=C+1; if(C%n==0, C=C+1); B=A; A=floor(A*(C+1)/C)); 1+A)}; a(n) = sum(k=0, n, A112564(n-k, k)); \\ Michel Marcus, Apr 23 2013

Crossrefs

Cf. A000960, A112564.

Sequence in context: A192923 A192673 A193021 * A301706 A289845 A101463

Adjacent sequences: A112566 A112567 A112568 * A112570 A112571 A112572

Keyword

more,nonn

Author

Paul D. Hanna, Oct 14 2005

Extensions

More terms from R. J. Mathar, Sep 26 2006

Status

approved