Tetris sequence generator. Live demo: http://jsfiddle.net/8zsrwm36/

tetris.js

var pieces = 'OISZLJT';

function tetrisGenerator(length) {
    var piecesArray = pieces.split('');
    var output = '';

    while (output.length < length) {
        // Shuffle the pieces (Fisher-Yates/Knuth shuffle: http://stackoverflow.com/a/2450976/3690621)
        var current = piecesArray.length, temp, random;
        while (current !== 0) {
            random = Math.floor(Math.random() * current);
            current -= 1;
            temp = piecesArray[current];
            piecesArray[current] = piecesArray[random];
            piecesArray[random] = temp;
        }

        // Append shuffled pieces
        output += piecesArray.join('');
    }

    // Return string trimmed to requested length
    return output.substring(0, length);
}

function validate(tetris) {
    // Number of tetris sections, disregarding remainders; e.g. 50 -> 7
    var sections = (tetris.length - (tetris.length % pieces.length)) / pieces.length;

    // Test each section
    for (var i = 0, validSection = false; i < sections; i++) {
        validSection = testSection(tetris.substring(i * pieces.length, (i + 1) * pieces.length));
        if (!validSection) {
            return false;
        }
    }

    // Then test the remainder (if it exists)
    var remainder = tetris.substring(tetris.length - (tetris.length % pieces.length), tetris.length);
    if (remainder.length > 0) {
        return testSection(remainder);
    }
    return true;

    // Test a tetromino section
    function testSection(section) {
        switch (section.length) {
            case 1:
                return pieces.indexOf(section) >= 0;
            case 7:
                return pieces.split('').sort().join('').indexOf(section.split('').sort().join('')) >= 0;
            default: // length: 0, 2-6, 8+
                if (section.length < 1 || section.length > 7) return false;

                for (var i = 0; i < section.length; i++) {
                    if (section.charAt(i) == section.charAt(i+1)) {
                        console.log('dupe');
                        return false; // There's a duplicated entry
                    }
                    
                    if (pieces.indexOf(section.charAt(i)) < 0) {
                        return false; // Item is not a valid tetromino
                    }
                }

                // Can't find any faults
                return true;
        }
    }
}

var tetrisString = tetrisGenerator(50);
console.log("'" + tetrisString + "' is" + (validate(tetrisString) ? '' : ' not') + ' valid');