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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.

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. A112564, A000960.

Sequence in context: A192923 A192673 A193021 * A101463 A206301 A026776

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 December 8 12:55 EST 2016. Contains 278945 sequences.