Data commit

Task/Fibonacci-n-step-number-sequences/Sidef/fibonacci-n-step-number-sequences-1.sidef

@@ -0,0 +1,13 @@
+func fib(n, xs=[1], k=20) {
+    loop {
+        var len = xs.len
+        len >= k && break
+        xs << xs.ft(max(0, len - n)).sum
+    }
+    return xs
+}
+
+for i in (2..10) {
+    say fib(i).join(' ')
+}
+say fib(2, [2, 1]).join(' ')

Task/Fibonacci-n-step-number-sequences/Sidef/fibonacci-n-step-number-sequences-2.sidef

@@ -0,0 +1,14 @@
+func fibonacci_matrix(k) is cached {
+    Matrix.build(k,k, {|i,j|
+        ((i == k-1) || (i == j-1)) ? 1 : 0
+    })
+}
+
+func fibonacci_kth_order(n, k=2) {
+    var A = fibonacci_matrix(k)
+    (A**n)[0][-1]
+}
+
+for k in (2..9) {
+    say ("Fibonacci of k=#{k} order: ", (15+k).of { fibonacci_kth_order(_, k) })
+}

Task/Fibonacci-n-step-number-sequences/Sidef/fibonacci-n-step-number-sequences-3.sidef

@@ -0,0 +1,20 @@
+func fibonacci_kth_order (n, k = 2) {
+
+    return 0 if (n < k-1)
+
+    var f = (1..(k+1) -> map {|j|
+        j < k ? 2**j : 1
+    })
+
+    k += 1
+
+    for i in (2*(k-1) .. n) {
+        f[i%k] = (2*f[(i-1)%k] - f[i%k])
+    }
+
+    return f[n%k]
+}
+
+for k in (2..9) {
+    say ("Fibonacci of k=#{k} order: ", (15+k).of { fibonacci_kth_order(_, k) })
+}