A290707 a(n) = 2^(n+1) + n^2 - 1.

1, 4, 11, 24, 47, 88, 163, 304, 575, 1104, 2147, 4216, 8335, 16552, 32963, 65760, 131327, 262432, 524611, 1048936, 2097551, 4194744, 8389091, 16777744, 33555007, 67109488, 134218403, 268436184, 536871695, 1073742664, 2147484547, 4294968256, 8589935615

Offset: 0

Author

Eric W. Weisstein, Aug 09 2017

Keywords

• nonn
• easy

Comments

For n > 1, also the number of irredundant sets in the complete bipartite graph K_{n,n}.

For n > 1, also the number of irredundant sets in the 2 X n rook graph. - Andrew Howroyd, Aug 11 2017

Links

• Eric Weisstein's World of Mathematics, Complete Bipartite Graph.
• Eric Weisstein's World of Mathematics, Irredundant Set.
• Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Crossrefs

Cf. A290709, A290818.

Programs

Mathematica

Table[2^(n + 1) + n^2 - 1, {n, 0, 40}]
LinearRecurrence[{5, -9, 7, -2}, {4, 11, 24, 47}, {0, 20}]
CoefficientList[Series[(1 - x - 2 x^3)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]

PARI

a(n)=2^(n+1)+n^2-1 \\ Charles R Greathouse IV, Aug 09 2017

Formula

a(n) = 2^(n+1) + n^2 - 1.

a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).

G.f.: x*(1 - x - 2*x^3)/((-1 + x)^3*(-1 + 2*x)).

E.g.f.: exp(x)*(x^2 + x - 1 + 2*exp(x)). - Elmo R. Oliveira, Mar 06 2025