A050227 - OEIS (original) (raw)

1, 3, 1, 7, 3, 1, 15, 8, 3, 1, 31, 19, 8, 3, 1, 63, 43, 20, 8, 3, 1, 127, 94, 47, 20, 8, 3, 1, 255, 201, 107, 48, 20, 8, 3, 1, 511, 423, 238, 111, 48, 20, 8, 3, 1, 1023, 880, 520, 251, 112, 48, 20, 8, 3, 1, 2047, 1815, 1121, 558, 255, 112, 48, 20, 8, 3, 1

REFERENCES

W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 2nd ed. New York: Wiley, p. 300, 1968.

LINKS

Eric Weisstein's World of Mathematics, Coin Tossing.

Eric Weisstein's World of Mathematics, Run.

EXAMPLE

Triangle begins:

1;

3, 1;

7, 3, 1;

15, 8, 3, 1;

31, 19, 8, 3, 1

...

MATHEMATICA

Clear[fib]; fib[n_, n_] = 1; fib[n_, k_] /; k > n = 0; fib[n_, k_] := fib[n, k] = If[k == 1, 1, Sum[fib[m, k], {m, n - k, n - 1}]]; Table[ 2^n - fib[n + k + 1, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jan 15 2013 *)