A319870 a(n) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18*17*16*15*14*13 + ... + (up to the n-th term).
6, 30, 120, 360, 720, 720, 732, 852, 2040, 12600, 95760, 666000, 666018, 666306, 670896, 739440, 1694160, 14032080, 14032104, 14032632, 14044224, 14287104, 19132560, 110941200, 110941230, 110942070, 110965560, 111598920, 128041920, 538459200, 538459236
Offset: 1
Examples
a(1) = 6; a(2) = 6*5 = 30; a(3) = 6*5*4 = 120; a(4) = 6*5*4*3 = 360; a(5) = 6*5*4*3*2 = 720; a(6) = 6*5*4*3*2*1 = 720; a(7) = 6*5*4*3*2*1 + 12 = 732; a(8) = 6*5*4*3*2*1 + 12*11 = 852; a(9) = 6*5*4*3*2*1 + 12*11*10 = 2040; a(10) = 6*5*4*3*2*1 + 12*11*10*9 = 12600; a(11) = 6*5*4*3*2*1 + 12*11*10*9*8 = 95760; a(12) = 6*5*4*3*2*1 + 12*11*10*9*8*7 = 666000; a(13) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18 = 666018; a(14) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18*17 = 666306; a(15) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18*17*16 = 670896; a(16) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18*17*16*15 = 739440; a(17) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18*17*16*15*14 = 1694160; a(18) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18*17*16*15*14*13 = 14032080; a(19) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18*17*16*15*14*13 + 24 = 14032104; a(20) = 6*5*4*3*2*1 + 12*11*10*9*8*7 + 18*17*16*15*14*13 + 24*23 = 14032632; etc.
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
Crossrefs
Programs
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Maple
a:=(n,k)->add((floor((n-j)/k)-floor((n-j-1)/k))*(mul(n-i-j+k+1,i=1..j)),j=1..k-1) + add((floor(j/k)-floor((j-1)/k))*(mul(j-i+1,i=1..k)),j=1..n): seq(a(n,6),n=1..35); # Muniru A Asiru, Sep 30 2018
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Mathematica
k:=6; a[n_]:=Sum[(Floor[(n-j)/k]-Floor[(n-j-1)/k])*Product[n-i-j+k+1, {i,1,j }] , {j,1,k-1} ] + Sum[(Floor[j/k]-Floor[(j-1)/k])*Product[j-i+1, {i,1,k}], {j,1,n}]; Array[a, 50] (* Stefano Spezia, Sep 30 2018 *)
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