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A191832 Number of solutions to the Diophantine equation x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 = n, with all xi >= 1. 1
0, 0, 0, 0, 1, 2, 7, 10, 22, 29, 51, 61, 99, 115, 163, 192, 262, 287, 385, 428, 528, 600, 730, 780, 963, 1054, 1202, 1337, 1545, 1646, 1908, 2059, 2269, 2516, 2770, 2933, 3298, 3568, 3792, 4142, 4493, 4786, 5183, 5562, 5831, 6423, 6745, 7140, 7639, 8231, 8479, 9216, 9603, 10260, 10663, 11488, 11752, 12838, 13100, 13887 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Related to "Liouville's Last Theorem".

LINKS

Robert Israel, Table of n, a(n) for n = 1..1000

George E. Andrews, Stacked lattice boxes, Ann. Comb. 3 (1999), 115-130. See L_5(n).

MAPLE

with(numtheory);

D00:=n->add(tau(j)*tau(n-j), j=1..n-1);

D01:=n->add(tau(j)*sigma(n-j), j=1..n-1);

D000:=proc(n) local t1, i, j;

t1:=0;

for i from 1 to n-1 do

for j from 1 to n-1 do

if (i+j < n) then t1 := t1+numtheory:-tau(i)*numtheory:-tau(j)*numtheory:-tau(n-i-j); fi;

od; od;

t1;

end;

L5:=n->D000(n)/6+D00(n)+D01(n)/2+(2*n-1/6)*tau(n)-11*sigma[2](n)/6;

[seq(L5(n), n=1..60)];

# Alternate:

g:= proc(n, k, j) option remember;

     if n < k-1 then 0

     elif k = 2 then

        if n mod j = 0 then 1 else 0 fi

     else

        add(procname(n-j*x, k-1, x), x=1 .. floor((n-k+2)/j))

     fi

end proc:

f:= n -> add(g(n, 6, j), j=1..n-4);

seq(f(n), n=1..100); # Robert Israel, Dec 02 2015

MATHEMATICA

g[n_, k_, j_] := g[n, k, j] = If[n < k - 1, 0, If[k == 2, If[ Mod[n, j] == 0, 1, 0], Sum[g[n - j x, k - 1, x], {x, 1, Floor[(n - k + 2)/j]}]]];

f[n_] := Sum[g[n, 6, j], {j, 1, n - 4}];

Array[f, 100] (* Jean-Fran├žois Alcover, Sep 25 2020, after Robert Israel *)

CROSSREFS

Cf. A000005, A000203, A002133, A055507, A191822, A191829, A191831.

Sequence in context: A270879 A022302 A023855 * A066964 A066967 A222450

Adjacent sequences:  A191829 A191830 A191831 * A191833 A191834 A191835

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 17 2011

STATUS

approved

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Last modified May 14 07:13 EDT 2021. Contains 343879 sequences. (Running on oeis4.)