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 A112569 Antidiagonal sums of square table A112564 of generalized Flavius Josephus sieves. 6
 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 (list; graph; refs; listen; history; text; internal format)
 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 #include 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

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Last modified June 10 03:15 EDT 2023. Contains 363186 sequences. (Running on oeis4.)