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

1,1

Comments

For similar multiply/add sequences in descending blocks of k natural numbers, we have: a(n) = Sum_{j=1..k-1} (floor((n-j)/k)-floor((n-j-1)/k)) * (Product_{i=1..j} n-i-j+k+1) + Sum_{j=1..n} (floor(j/k)-floor((j-1)/k)) * (Product_{i=1..k} j-i+1). Here, k=6.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Example

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.

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

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 *)

Crossrefs

For similar sequences, see: A000217 (k=1), A319866 (k=2), A319867 (k=3), A319868 (k=4), A319869 (k=5), this sequence (k=6), A319871 (k=7), A319872 (k=8), A319873 (k=9), A319874 (k=10).

Sequence in context: A117489 A050510 A319889 * A055281 A346174 A182349

Adjacent sequences: A319867 A319868 A319869 * A319871 A319872 A319873

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Sep 30 2018

Status

approved