Template:Tiara pair Clay/wave

integer weight

w a 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 sums 0 1 1 2 1 1 2 1 4 2 1 4 6 4 1 16 3 1 8 28 56 70 56 28 8 1 256 4 1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1 65536 5 1 32 496 4960 35960 201376 906192 3365856 10518300 28048800 64512240 129024480 225792840 347373600 471435600 565722720 601080390 565722720 471435600 347373600 225792840 129024480 64512240 28048800 10518300 3365856 906192 201376 35960 4960 496 32 1 4294967296

rational weight

w a $0$ ${\frac {1}{32}}$ ${\frac {1}{16}}$ ${\frac {3}{32}}$ ${\frac {1}{8}}$ ${\frac {5}{32}}$ ${\frac {3}{16}}$ ${\frac {7}{32}}$ ${\frac {1}{4}}$ ${\frac {9}{32}}$ ${\frac {5}{16}}$ ${\frac {11}{32}}$ ${\frac {3}{8}}$ ${\frac {13}{32}}$ ${\frac {7}{16}}$ ${\frac {15}{32}}$ ${\frac {1}{2}}$ ${\frac {17}{32}}$ ${\frac {9}{16}}$ ${\frac {19}{32}}$ ${\frac {5}{8}}$ ${\frac {21}{32}}$ ${\frac {11}{16}}$ ${\frac {23}{32}}$ ${\frac {3}{4}}$ ${\frac {25}{32}}$ ${\frac {13}{16}}$ ${\frac {27}{32}}$ ${\frac {7}{8}}$ ${\frac {29}{32}}$ ${\frac {15}{16}}$ ${\frac {31}{32}}$ $1$ sums 0 1 1 2 1 1 2 1 4 2 1 4 6 4 1 16 3 1 8 28 56 70 56 28 8 1 256 4 1 16 120 560 1820 4368 8008 11440 12870 11440 8008 4368 1820 560 120 16 1 65536 5 1 32 496 4960 35960 201376 906192 3365856 10518300 28048800 64512240 129024480 225792840 347373600 471435600 565722720 601080390 565722720 471435600 347373600 225792840 129024480 64512240 28048800 10518300 3365856 906192 201376 35960 4960 496 32 1 4294967296

unit fractions
w a $1$ ${\frac {1}{2}}$ ${\frac {1}{4}}$ ${\frac {1}{8}}$ ${\frac {1}{16}}$ ${\frac {1}{32}}$ sums 0 1 1 1 1 2 3 2 1 6 4 11 3 1 70 28 8 107 4 1 12870 1820 120 16 14827 5 1 601080390 10518300 35960 496 32 611635179

plain text

rows: [ 1, 1], [ 1, 2, 1], [ 1, 4, 6, 4, 1], [ 1, 8, 28, 56, 70, 56, 28, 8, 1], [ 1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1], [ 1, 32, 496, 4960, 35960, 201376, 906192, 3365856, 10518300, 28048800, 64512240, 129024480, 225792840, 347373600, 471435600, 565722720, 601080390, 565722720, 471435600, 347373600, 225792840, 129024480, 64512240, 28048800, 10518300, 3365856, 906192, 201376, 35960, 4960, 496, 32, 1] central values:   (rational weight = 1/2) [2, 6, 70, 12870, 601080390] diagonal:   (integer weight = arity) [ 1, 2, 6, 56, 1820, 201376] row sums: [2, 4, 16, 256, 65536, 4294967296] unit fractions: [1], [1, 2], [1, 6, 4], [1, 70, 28, 8], [1, 12870, 1820, 120, 16], [1, 601080390, 10518300, 35960, 496, 32] row sums of unit fractions: [1, 3, 11, 107, 14827, 611635179]

content above, documentation below

All Boolean functions by weight. Row $arity$ of this triangle is row $2^{arity}$ of Pascal's triangle.