A290699 a(n) = 2^n - n + n^2.

0, 2, 6, 14, 28, 52, 94, 170, 312, 584, 1114, 2158, 4228, 8348, 16566, 32978, 65776, 131344, 262450, 524630, 1048956, 2097572, 4194766, 8389114, 16777768, 33555032, 67109514, 134218430, 268436212, 536871724, 1073742694, 2147484578, 4294968288, 8589935648, 17179870306

Offset: 0

Author

Eric W. Weisstein, Aug 09 2017

Keywords

• nonn
• easy

Comments

Number of minimal edge covers in the n-book graph.

Links

• Eric Weisstein's World of Mathematics, Book Graph
• Eric Weisstein's World of Mathematics, Minimal Edge Cover
• Index entries for linear recurrences with constant coefficients, signature (5, -9, 7, -2).

Crossrefs

Cf. A132109.

A077265 is a subsequence.

Programs

Mathematica

Table[2^n - n + n^2, {n, 20}]
LinearRecurrence[{5, -9, 7, -2}, {2, 6, 14, 28}, 20]
CoefficientList[Series[-((2 (-1 + 2 x - x^2 + x^3))/((-1 + x)^3 (-1 + 2 x))), {x, 0, 20}], x]

Formula

a(n) = 2*A132109(n-1).

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

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

Extensions

Added a(0)=0. - N. J. A. Sloane, May 25 2019