A356770 a(n) is the number of equations in the set {x+2y=n, 2x+3y=n, ..., k*x+(k+1)*y=n, ..., n*x+(n+1)*y=n} which admit at least one nonnegative integer solution.

1, 2, 3, 4, 4, 5, 5, 6, 6, 7, 6, 8, 7, 8, 8, 9, 8, 10, 8, 10, 10, 10, 9, 12, 10, 11, 11, 12, 10, 13, 11, 13, 12, 12, 12, 15, 12, 13, 13, 15, 12, 15, 13, 15, 15, 14, 13, 17, 14, 16, 15, 16, 14, 17, 15, 17, 16, 16, 15, 20, 15, 16, 17, 18, 17, 19, 16, 18, 17, 19, 16, 21, 17, 18, 19, 19

Offset

1,2

Comments

a(n) = ceiling(2*(sqrt(n)-1)) + ceiling(A000005(n)/2).

Links

Table of n, a(n) for n=1..76.

Example

a(5) = 4. Consider the equations: x+2y=5, 2x+3y=5, 3x+4y=5, 4x+5y=5, 5x+6y=5. Only four of them admit at least one nonnegative integer solution, since 3x+4y=5 has no nonnegative integer solution.

Mathematica

b[m_] := m;
f[n_] := Table[Dimensions[Solve[b[k]*x + b[k + 1]*y == n, {x, y}, NonNegativeIntegers]][[1]], {k, 1, n}];
Flatten[Table[Dimensions[DeleteCases[f[k], 0]], {k, 1, 100}]]

Crossrefs

Cf. A000005.

Sequence in context: A196162 A071940 A085883 * A265912 A094192 A093874

Adjacent sequences: A356767 A356768 A356769 * A356771 A356772 A356773

Keyword

nonn

Author

Luca Onnis, Aug 27 2022

Status

approved