A024873 a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers >= 2), t = (Lucas numbers).

6, 8, 26, 43, 97, 156, 308, 499, 915, 1480, 2598, 4204, 7178, 11614, 19476, 31513, 52219, 84492, 138900, 224745, 367509, 594642, 968924, 1567752, 2548478, 4123524, 6692462, 10828631, 17556405, 28406860, 46023972, 74468351, 120596327, 195128956, 315902914

Offset

2,1

Links

Table of n, a(n) for n=2..36.

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

Formula

G.f.:(-6+2*x^7+x^6+4*x^5+2*x^4-5*x^3-2*x)/((x^2+x-1)*(x^4+x^2-1)^2) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]

a(0)=6, a(1)=8, a(2)=26, a(3)=43, a(4)=97, a(5)=156, a(6)=308, a(7)=499, a(8)=915, a(9)=1480, a(n)=a(n-1)+3*a(n-2)-2*a(n-3)-a(n-4)-a(n-5)- 3*a(n-6)+2*a(n-7)+a(n-8)+a(n-9)+a(n-10) [From Harvey P. Dale, May 19 2011]

Mathematica

LinearRecurrence[{1, 3, -2, -1, -1, -3, 2, 1, 1, 1}, {6, 8, 26, 43, 97, 156, 308, 499, 915, 1480}, 50] (* or *) CoefficientList[ Series[ (-6+2x^7+x^6+4x^5+2x^4- 5x^3-2x)/((x^2+x-1)(x^4+x^2-1)^2), {x, 0, 50}], x] (* Harvey P. Dale, May 19 2011 *)

Crossrefs

Sequence in context: A155478 A219191 A107366 * A066231 A267477 A237290

Adjacent sequences: A024870 A024871 A024872 * A024874 A024875 A024876

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Harvey P. Dale, May 19 2011.

Status

approved