A298677 a(n) = 110*a(n-1) - a(n-2) for n >= 2, a(0)=1, a(1)=111.

1, 111, 12209, 1342879, 147704481, 16246150031, 1786928798929, 196545921732159, 21618264461738561, 2377812544869509551, 261537761671184312049, 28766775971285404815839, 3164083819079723345430241, 348020453322798282592510671, 38279085781688731361830743569, 4210351415532437651518789281919

Offset

0,2

Comments

Sequence {s_k(110)} of A269254.

The sequence contains no primes; see A269254 for a proof by N. J. A. Sloane.

For detailed theory, see [Hone]. - L. Edson Jeffery, Feb 09 2018

Links

Colin Barker, Table of n, a(n) for n = 0..450

Index entries for linear recurrences with constant coefficients, signature (110,-1).

Andrew N. W. Hone, et al., On a family of sequences related to Chebyshev polynomials, arXiv:1802.01793 [math.NT], 2018.

Formula

G.f.: (1 + x)/(1 - 110*x + x^2).

a(n) = (1/18)*((55+12*sqrt(21))^(-n)*(9-2*sqrt(21) + (9+2*sqrt(21))*(55+12*sqrt(21))^(2*n))). - Colin Barker, Jan 25 2018

Mathematica

s[0, n_] := 1; s[1, n_] := n + 1; s[k_, n_] := n*s[k - 1, n] - s[k - 2, n]; Table[s[k, 110], {k, 0, 15}]
LinearRecurrence[{110, -1}, {1, 111}, 15]
CoefficientList[Series[(1 + x)/(1 - 110*x + x^2), {x, 0, 14}], x]

Prog

(PARI) Vec((1 + x)/(1 - 110*x + x^2) + O(x^20)) \\ Colin Barker, Jan 25 2018

Crossrefs

Cf. A285992, A299107, A299109, A088165, A117522, A299100, A299101, A113501, A269253, A269254, A294099, A298675, A298677, A298878, A299045, A299071.

Sequence in context: A349805 A165155 A078270 * A172175 A178906 A225374

Adjacent sequences: A298674 A298675 A298676 * A298678 A298679 A298680

Keyword

nonn,easy

Author

L. Edson Jeffery, Bob Selcoe and Andrew Hone, Jan 24 2018

Status

approved