A sequence with additional state https://gist.github.com/vritant24/0e39482ac2c91f6368d1f13eaacaf2b0

StatefulSequence.cs

using System;
using System.Collections;
using System.Collections.Generic;

namespace Streamable
{
    public class Sequence<T, U> : IEnumerable<T>, IEnumerator<T>
    {
        private readonly Func<T, U, ulong, (T element, U state, bool isLast)> formulae;
        private readonly T firstElement;
        private readonly U initialState;
        private bool isEnded;
        private ulong index;

        private readonly object valueGate = new();

        public Sequence(
            Func<T, U, ulong, (T nextElement, U state, bool isLast)> formulae,
            T firstElement,
            U initialState)
        {
            this.formulae = formulae;
            this.firstElement = firstElement;
            this.initialState = initialState;

            this.isEnded = false;
            this.index = 0;
            this.Current = this.firstElement;
            this.State = this.initialState;
        }

        #region IEnumerator
        public T Current { get; private set; }

        public U State { get; private set; }

        object IEnumerator.Current => Current;

        public bool MoveNext()
        {
            lock (valueGate)
            {
                if (isEnded)
                {
                    return false;
                }

                this.index++;
                (Current, State, isEnded) = formulae(Current, State, this.index);
            }
            return true;
        }

        public void Reset()
        {
            lock (valueGate)
            {
                this.isEnded = false;
                this.index = 0;
                this.Current = this.firstElement;
                this.State = this.initialState;
            }
        }

        public void Dispose()
        {
            // Do nothing
        }
        #endregion

        #region IEnumerable
        public IEnumerator<T> GetEnumerator()
        {
            return this;
        }

        IEnumerator IEnumerable.GetEnumerator()
        {
            return this;
        }
        #endregion
    }
}