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

%I A265826 #35 Mar 30 2022 06:12:54
%S A265826 1,1,2,4,7,13,24,45,84,157,293,547,1021,1906,3558,6642,12399,23146,
%T A265826 43208,80659,150571,281080,524709,979506,1828503,3413376,6371955,
%U A265826 11894912,22204949,41451316,77379669,144449290,269652192,503375992,939682290
%N A265826 a(0) = 1, a(n) = Sum_{k=1..n} a(n-k)*ceiling(sin(k)).
%C A265826 It appears that a(n) <= A088353(n). They are identical until n=11 where a(11) = 547, but A088353(n) = 548.
%C A265826 It also appears that a(n) <= A059633(n+2). They are identical until n=25 where a(25) = 3413376, but A059633(27) = 3413377.
%H A265826 Griffin N. Macris, <a href="/A265826/b265826.txt">Table of n, a(n) for n = 0..999</a>
%F A265826 a(0) = 1
%F A265826 a(n) = Sum_{k=1..n} a(n-k)*ceiling(sin(k)).
%e A265826 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.
%t A265826 A[0] := 1
%t A265826 A[n_] := A[n] = If[n <= 0, 0, Sum[A[n - k]Ceiling[Sin[k]], {k, 1, n}]]
%o A265826 (Java)
%o A265826 int limit = 500; //limit index, can be changed for more terms
%o A265826 BigInteger[] n = new BigInteger[limit];
%o A265826 n[0] = BigInteger.ONE;
%o A265826 System.out.println("0 1");
%o A265826 for ( int i = 1; i < n.length; i++ ) {
%o A265826    n[i] = BigInteger.ZERO;
%o A265826    for(int k = 1; k <= i; k++) {
%o A265826       n[i] = n[i].add(n[i-k].multiply(BigInteger.valueOf((long) Math.ceil(Math.sin(k)))));
%o A265826    }
%o A265826    System.out.println(i+" "+n[i]);
%o A265826 }
%K A265826 nonn,easy
%O A265826 0,3
%A A265826 _Griffin N. Macris_, Apr 06 2016