A265826 a(0) = 1, a(n) = Sum_{k=1..n} a(n-k)*ceiling(sin(k)).

1, 1, 2, 4, 7, 13, 24, 45, 84, 157, 293, 547, 1021, 1906, 3558, 6642, 12399, 23146, 43208, 80659, 150571, 281080, 524709, 979506, 1828503, 3413376, 6371955, 11894912, 22204949, 41451316, 77379669, 144449290, 269652192, 503375992, 939682290

Offset: 0

Author

Griffin N. Macris, Apr 06 2016

Keywords

• nonn
• easy

Comments

It appears that a(n) <= A088353(n). They are identical until n=11 where a(11) = 547, but A088353(n) = 548.

It also appears that a(n) <= A059633(n+2). They are identical until n=25 where a(25) = 3413376, but A059633(27) = 3413377.

Examples

			a(4) = 1*ceiling(sin(4)) + 1*ceiling(sin(3)) + 2*ceiling(sin(2)) + 4*ceiling(sin(1)) = 1*0 + 1*1 + 2*1 + 4*1 = 7.
		

Links

• Griffin N. Macris, Table of n, a(n) for n = 0..999

Programs

Java

int limit = 500; //limit index, can be changed for more terms
BigInteger[] n = new BigInteger[limit];
n[0] = BigInteger.ONE;
System.out.println("0 1");
for ( int i = 1; i < n.length; i++ ) {
   n[i] = BigInteger.ZERO;
   for(int k = 1; k <= i; k++) {
      n[i] = n[i].add(n[i-k].multiply(BigInteger.valueOf((long) Math.ceil(Math.sin(k)))));
   }
   System.out.println(i+" "+n[i]);
}

Mathematica

A[0] := 1
A[n_] := A[n] = If[n <= 0, 0, Sum[A[n - k]Ceiling[Sin[k]], {k, 1, n}]]

Formula

a(0) = 1

a(n) = Sum_{k=1..n} a(n-k)*ceiling(sin(k)).