Template:Boolf triangle Magnolia

rational weight

w a ${\displaystyle 0}$ ${\displaystyle {\frac {1}{32}}}$ ${\displaystyle {\frac {1}{16}}}$ ${\displaystyle {\frac {3}{32}}}$ ${\displaystyle {\frac {1}{8}}}$ ${\displaystyle {\frac {5}{32}}}$ ${\displaystyle {\frac {3}{16}}}$ ${\displaystyle {\frac {7}{32}}}$ ${\displaystyle {\frac {1}{4}}}$ ${\displaystyle {\frac {9}{32}}}$ ${\displaystyle {\frac {5}{16}}}$ ${\displaystyle {\frac {11}{32}}}$ ${\displaystyle {\frac {3}{8}}}$ ${\displaystyle {\frac {13}{32}}}$ ${\displaystyle {\frac {7}{16}}}$ ${\displaystyle {\frac {15}{32}}}$ ${\displaystyle {\frac {1}{2}}}$ ${\displaystyle {\frac {17}{32}}}$ ${\displaystyle {\frac {9}{16}}}$ ${\displaystyle {\frac {19}{32}}}$ ${\displaystyle {\frac {5}{8}}}$ ${\displaystyle {\frac {21}{32}}}$ ${\displaystyle {\frac {11}{16}}}$ ${\displaystyle {\frac {23}{32}}}$ ${\displaystyle {\frac {3}{4}}}$ ${\displaystyle {\frac {25}{32}}}$ ${\displaystyle {\frac {13}{16}}}$ ${\displaystyle {\frac {27}{32}}}$ ${\displaystyle {\frac {7}{8}}}$ ${\displaystyle {\frac {29}{32}}}$ ${\displaystyle {\frac {15}{16}}}$ ${\displaystyle {\frac {31}{32}}}$ ${\displaystyle 1}$ sums 0 1 1 2 1 0 1 1 2 2 0 1 4 4 1 10 3 0 1 13 44 67 56 28 8 1 218 4 0 1 40 360 1546 4144 7896 11408 12866 11440 8008 4368 1820 560 120 16 1 64594 5 0 1 121 2680 27550 180096 866432 3308736 10453960 27991600 64472200 129002640 225783740 347370800 471435000 565722640 601080385 565722720 471435600 347373600 225792840 129024480 64512240 28048800 10518300 3365856 906192 201376 35960 4960 496 32 1 4294642034

summation of {{Boolf triangle Myrtle}}

rational weight:

Let C be the central column. Then C(a) + a = 2 · A069954(a−1) = A000984(2^a−1) for a > 0.

integer weight:

Diagonal is A134174.

Column 2 is A003462.   a(n) = (3ⁿ − 1) / 2.

merged weights:

The diagonal 1, 5, 93, 26333... is half of A037267(1...) = 2, 10, 186, 52666...