A364655 Circuit rank and corank of the n-Pell graph.

0, 0, 1, 7, 30, 106, 339, 1021, 2956, 8324, 22965, 62371, 167306, 444302, 1170151, 3060409, 7956824, 20581576, 53000873, 135952639, 347525686, 885612402, 2250586811, 5705067061, 14429119332, 36418383564, 91744440541, 230719450651, 579286267938, 1452310024726

Offset

0,4

Links

Table of n, a(n) for n=0..29.

Eric Weisstein's World of Mathematics, Circuit Rank

Eric Weisstein's World of Mathematics, Corank

Eric Weisstein's World of Mathematics, Pell Graph

Index entries for linear recurrences with constant coefficients, signature (5,-6,-2,3,1).

Formula

a(n) = A000129(n)*(n/2 - 1) + 1.

a(n) = 5*a(n-1) - 6*a(n-2) - 2*a(n-3) + 3*a(n-4) + a(n-5).

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

Mathematica

Table[Fibonacci[n + 1, 2] (n/2 - 1) + 1, {n, 0, 20}]
CoefficientList[Series[-x^2 (1 + x)^2/((-1 + x) (-1 + 2 x + x^2)^2), {x, 0, 20}], x]
LinearRecurrence[{5, -6, -2, 3, 1}, {0, 0, 1, 7, 30}, 20]

Crossrefs

Sequence in context: A038798 A276289 A062455 * A368528 A085277 A269084

Adjacent sequences: A364652 A364653 A364654 * A364656 A364657 A364658

Keyword

nonn

Author

Eric W. Weisstein, Jul 31 2023

Status

approved