A249863 Chebyshev S polynomial (A049310) evaluated at x = 26/7 and multiplied by powers of 7 (A000420).

1, 26, 627, 15028, 360005, 8623758, 206577463, 4948449896, 118537401609, 2839498396930, 68018625641339, 1629348845225244, 39030157319430733, 934945996889162102, 22396118210466108735, 536486719624549884112

Offset: 0

Author

Wolfdieter Lang, Nov 09 2014

Keywords

• nonn
• easy

Comments

This sequence appears in the solution of the curvature sequence of the touching circle and chord example given by Kival Ngaokrajang in A249458. See also the pair A249864(n) and a(n-1), with a(-1) = 0, for which details are given in A249864.

Links

• Index entries for linear recurrences with constant coefficients, signature (26,-49)
• Index entries for sequences related to Chebyshev polynomials

Crossrefs

Cf. A000420, A049310, A249864, A248163.

Programs

Magma

I:=[1,26]; [n le 2 select I[n] else 26*Self(n-1)-49*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Nov 09 2014

Mathematica

LinearRecurrence[{26,-49},{1,26},20] (* Harvey P. Dale, Jun 30 2017 *)

Formula

a(n) = 7^n*S(n, 26/7) with Chebyshev's S polynomial (for S see the coefficient triangle A049310).

O.g.f.: 1/(1 - 26*x + (7*x)^2).

a(n) = 26*a(n-1) - 49*a(n-2), a(-1) = 0, a(0) = 1 .