数学吧 关注：894,277贴子：8,762,003
a君的4拆分数公式:
f₄(n)=n^3/144+n^2/48-n/32-13/288+(-1)^n×n/32+(-1)^n×n/32-1/9cos(2nπ/3)+1/27×√3sin(2nπ/3)+1/8cos(nπ/2)
f₄(n)=n^3/144+n^2/48-n/32-13/288+(-1)^n×n/32+(-1)^n×n/32-1/9cos(2nπ/3)+1/27×√3sin(2nπ/3)+1/8cos(nπ/2)
n=4
f₄(4)=4³/144+4²/48-4/32-13/288+4/32+1/32-1/9×(-1/2)+1/27×√3(√3/2)+1/8×1=(128+96-36-13+36+9+16+16+36)/288=288/288=1
f₄(4)=4³/144+4²/48-4/32-13/288+4/32+1/32-1/9×(-1/2)+1/27×√3(√3/2)+1/8×1=(128+96-36-13+36+9+16+16+36)/288=288/288=1
上接第19楼
n=5
f₄(5)=5³/144+5²/48-5/32-13/288-5/32-1/32-1/9(-1/2)+1/27×(-3/2)+1/8×0=(250+150-45-13-45-9+16-16+0)/288=1
n=5
f₄(5)=5³/144+5²/48-5/32-13/288-5/32-1/32-1/9(-1/2)+1/27×(-3/2)+1/8×0=(250+150-45-13-45-9+16-16+0)/288=1
n=6
f₄(6)=6³/144+6²/48-6/32-13/288+6/32+1/32-1/9×1+1/27×√3×0+1/8×(-1)=(432+216-54-13+54+9-32-36)/288=2
f₄(6)=6³/144+6²/48-6/32-13/288+6/32+1/32-1/9×1+1/27×√3×0+1/8×(-1)=(432+216-54-13+54+9-32-36)/288=2
n=523
f₄(523)=526³/144+523²/48-523/32-13/288-523/32-1/32-1/9(-1/2)+1/27×3/2+1/8×0=(286111334+1641174-4707-13-4707-9+16+16+0)/288=999108
f₄(523)=526³/144+523²/48-523/32-13/288-523/32-1/32-1/9(-1/2)+1/27×3/2+1/8×0=(286111334+1641174-4707-13-4707-9+16+16+0)/288=999108
n=20240504
f₄(20240504)=20240504³/144+20240504²/48-20240504/32-13/288+20240504/32+1/32-1/9(-1/2)+1/27(-3/2)+1/8(-1/2)=(16584178483430359088128+2458068013044096-182164536-13+182164536+9+16-16+36)/288=57583961602424903237
f₄(20240504)=20240504³/144+20240504²/48-20240504/32-13/288+20240504/32+1/32-1/9(-1/2)+1/27(-3/2)+1/8(-1/2)=(16584178483430359088128+2458068013044096-182164536-13+182164536+9+16-16+36)/288=57583961602424903237
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