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 A130695 Number of ways to write n as (a+1)(b+1)(c+1) - abc with a, b, c nonnegative integers. 4
 1, 3, 3, 6, 3, 9, 4, 9, 6, 12, 3, 15, 6, 12, 9, 15, 3, 21, 7, 15, 9, 18, 6, 24, 9, 15, 9, 24, 6, 30, 6, 15, 15, 24, 9, 30, 7, 21, 12, 30, 3, 33, 15, 21, 15, 24, 6, 39, 12, 27, 12, 27, 9, 42, 12, 21, 15, 36, 6, 45, 13, 18, 21, 36, 12, 39, 6, 33, 15, 45, 9, 42, 12, 24, 24, 30, 9, 57, 18, 30 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS _Jan Kristian Haugland_, Jul 10 2007, Table of n, a(n) for n = 1..200 FORMULA a(2*n) = A238872(2*n) / 3 if n>0. a(2*n + 1) = A238872(2*n + 1). - Michael Somos, Jul 04 2015 EXAMPLE a(7) = 4 because 7 = 7*1*1-6*0*0 = 1*7*1-0*6*0 = 1*1*7-0*0*6 = 2*2*2-1*1*1. G.f. = x + 3*x^2 + 3*x^3 + 6*x^4 + 3*x^5 + 9*x^6 + 4*x^7 + 9*x^8 + 6*x^9 + ... MATHEMATICA f[{a_, b_, c_}]:=(a+1)(b+1)(c+1)-a*b*c; nn=80; Take[Transpose[Sort[Tally[f/@ Tuples[Range[0, nn], 3]], #1[[1]]<#2[[1]]&]] [[2]], nn] (* Harvey P. Dale, Mar 05 2012 *) a[ n_] := Length @ FindInstance[ {x >= 0, y >= 0, z >= 0, x y + y z + z x + x + y + z + 1 == n}, {x, y, z}, Integers, 10^9]; (* Michael Somos, Jul 04 2015 *) a[ n_] := (2 + (-1)^n) Length @ FindInstance[ {1 <= y <= n, 1 <= x <= y, 1 <= z <= y, y^2 - (x^2 - x + z^2 - z) / 2 == n}, {x, y, z}, Integers, 10^9]; (* Michael Somos, Jul 04 2015 *) CROSSREFS Cf. A238872. Sequence in context: A007425 A260152 A358223 * A308083 A181788 A112163 Adjacent sequences: A130692 A130693 A130694 * A130696 A130697 A130698 KEYWORD nonn AUTHOR Jan Kristian Haugland, Jul 10 2007 STATUS approved

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Last modified March 29 18:41 EDT 2023. Contains 361599 sequences. (Running on oeis4.)