Fill the series 5,7,17,47,115,? find the value in the "?".
The function is:
an=(n−10)⋅d0+(n−11)⋅d1+(n−12)⋅d2+(n−13)⋅d3+(n−14)⋅d4an=d0+(n−1)d1+12(n−1)(n−2)d2+13⋅12(n−1)(n−2)(n−3)d3+14⋅13⋅12(n−1)(n−2)(n−3)(n−4)d4an=d0+(n−1){d1+(n−2)[12d2+(n−3)(16d3+124(n−4)d4)]}…an=d0−d1+d2−d3+d4+n⋅(12d1−18d2+22d3−25d412)+n2⋅(12d2−24d3+35d424)+n3⋅(4d3−10d424)+n4⋅(d424)
we have:
d0=5d1=2d2=8d3=12d4=6
an=d0−d1+d2−d3+d4+n⋅(12d1−18d2+22d3−25d412)+n2⋅(12d2−24d3+35d424)+n3⋅(4d3−10d424)+n4⋅(d424)an=5−2+8−12+6+n⋅(12⋅2−18⋅8+22⋅12−25⋅612)+n2⋅(12⋅8−24⋅12+35⋅624)+n3⋅(4⋅12−10⋅624)+n4⋅(624)an=5−12⋅n+34⋅n2−12⋅n3+14⋅n4an=5−12⋅n+34⋅n2−12⋅n3+14⋅n4
Very impressive but how did you work it out Alan?
It wasn't even in the oeis ....
Fill the series 5, 7, 17, 47, 115, ? find the value in the "?".
d0=571747115⋯1. Difference d1=2103068⋯2. Difference d2=82038⋯3. Difference d3=1218⋯4. Difference d4=6⋯
an=(n−10)⋅d0+(n−11)⋅d1+(n−12)⋅d2+(n−13)⋅d3+(n−14)⋅d4
an=(n−10)⋅5+(n−11)⋅2+(n−12)⋅8+(n−13)⋅12+(n−14)⋅6a6=(50)⋅5+(51)⋅2+(52)⋅8+(53)⋅12+(54)⋅6a6=1⋅5+5⋅2+10⋅8+10⋅12+5⋅6a6=5+10+80+120+30a6=245
Fill the series 5,7,17,47,115,? find the value in the "?".
The function is:
an=(n−10)⋅d0+(n−11)⋅d1+(n−12)⋅d2+(n−13)⋅d3+(n−14)⋅d4an=d0+(n−1)d1+12(n−1)(n−2)d2+13⋅12(n−1)(n−2)(n−3)d3+14⋅13⋅12(n−1)(n−2)(n−3)(n−4)d4an=d0+(n−1){d1+(n−2)[12d2+(n−3)(16d3+124(n−4)d4)]}…an=d0−d1+d2−d3+d4+n⋅(12d1−18d2+22d3−25d412)+n2⋅(12d2−24d3+35d424)+n3⋅(4d3−10d424)+n4⋅(d424)
we have:
d0=5d1=2d2=8d3=12d4=6
an=d0−d1+d2−d3+d4+n⋅(12d1−18d2+22d3−25d412)+n2⋅(12d2−24d3+35d424)+n3⋅(4d3−10d424)+n4⋅(d424)an=5−2+8−12+6+n⋅(12⋅2−18⋅8+22⋅12−25⋅612)+n2⋅(12⋅8−24⋅12+35⋅624)+n3⋅(4⋅12−10⋅624)+n4⋅(624)an=5−12⋅n+34⋅n2−12⋅n3+14⋅n4an=5−12⋅n+34⋅n2−12⋅n3+14⋅n4