The tetranacci numbers extend the Fibonacci idea one step further than the [[tribonacci]] numbers: each term is the sum of the preceding four. From seeds 0, 0, 0, 1 the sequence runs 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773, 1490.
The early terms shadow the powers of two (1, 2, 4, 8) before falling behind at 15. The ratio of consecutive terms converges to the tetranacci constant ≈ 1.9276, the largest real root of \(x^4 = x^3 + x^2 + x + 1\) — the four-step analogue of the golden ratio, edging closer to 2 as the number of summed terms grows.