Связь чисел Фибоначчи и числа "сочетаний"

REM
REM  1 23 4 56 78 9 ... N
REM
REM  Fibonachi AND "Sochetania"
REM
 
DECLARE FUNCTION f! (n!)
 
CLS
FOR i = 1 TO 20
   PRINT f(i)
NEXT
END
 
FUNCTION f (n)
   IF n <= 3 THEN
      f = n
   ELSE
      f = f(n - 1) + f(n - 2)
   END IF
END FUNCTION

DIM i AS LONG, n AS LONG, m AS DOUBLE, s AS DOUBLE
n = 20
FOR i = 0 TO n
    m = MyCombin(n, i)
    PRINT i, m
    s = s + m
NEXT i
PRINT s, 2 ^ n
 
FUNCTION MyCombin#(BYVAL n AS LONG, BYVAL m AS LONG)
    DIM i AS LONG
    IF m > n OR m < 0 THEN EXIT FUNCTION
    IF m > n - m THEN m = n - m
    MyCombin = 1
    FOR i = 1 TO m
        MyCombin = MyCombin * n / i
        n = n - 1
    NEXT i
END FUNCTION

DIM i AS LONG, n AS LONG, m AS DOUBLE, s AS DOUBLE
n = 20
m = 1
PRINT m
s = m
FOR i = 1 TO n
    m = m * (n + 1 - i) / i
    PRINT m
    s = s + m
NEXT i
PRINT s, 2 ^ n

DIM a(1 TO 20) AS LONG, i AS LONG, j AS LONG, m AS LONG, k AS LONG, n AS LONG, p AS LONG, txt AS STRING
n = 5 'количество чисел
m = n - 1 'количество запятых
FOR k = m TO 0 STEP -1 'перебираем запятые между числами, от n-1 зяпятых до 0
    IF k = 0 THEN 'если запятых нет, то просто выводим ряд чисел
        txt = ""
        FOR i = 1 TO n
            txt = txt + LTRIM$(STR$(i))
        NEXT i
        PRINT txt
    ELSE
        FOR i = 1 TO k: a(i) = i: NEXT i
        IF k = m THEN p = 1 ELSE p = k
        DO 'генерация всех сочетаний из m по k
            'вывод чисел
            j = 0
            txt = ""
            FOR i = 1 TO k
                WHILE j < a(i)
                    j = j + 1
                    txt = txt + LTRIM$(STR$(j))
                WEND
                txt = txt + ","
            NEXT i
            FOR i = j + 1 TO n
                txt = txt + LTRIM$(STR$(i))
            NEXT i
            PRINT txt
            
            IF a(k) = m THEN p = p - 1 ELSE p = k
            IF p THEN
                FOR i = k TO p STEP -1
                    a(i) = a(p) + i - p + 1
                NEXT i
            END IF
        LOOP WHILE p
    END IF
NEXT k
PRINT "Kol-vo:"; 2 ^ m

DIM i AS LONG, j AS LONG, n AS LONG, m AS LONG, txt AS STRING
n = 5 'количество чисел
FOR i = 0 TO 2 ^ (n - 1) - 1
    m = i
    txt = ""
    FOR j = 1 TO n
        txt = txt + LTRIM$(STR$(j))
        IF m MOD 2 THEN txt = txt + ","
        m = m \ 2
    NEXT j
    PRINT txt
NEXT i
PRINT "Kol-vo:"; 2 ^ (n - 1)