A330767 a(n) = 25*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 25.

2, 25, 627, 15700, 393127, 9843875, 246490002, 6172093925, 154548838127, 3869893047100, 96901875015627, 2426416768437775, 60757321085960002, 1521359443917437825, 38094743419021905627, 953889944919465078500, 23885343366405648868127, 598087474105060686781675, 14976072195992922818410002

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (25,1).

Formula

a(n) = ( (25 + sqrt(629))^n + (25 - sqrt(629))^n )/2^n.

G.f.: (2 - 25*x)/(1-25*x-x^2).

a(n) = Lucas(n, 25) = 2*(-i)^n * ChebyshevT(n, 25*i/2).

Maple

seq(simplify(2*(-I)^n*ChebyshevT(n, 25*I/2)), n = 0..25);

Mathematica

LucasL[Range[25] -1, 25]

Prog

(PARI) vector(26, n, 2*(-I)^(n-1)*polchebyshev(n-1, 1, 25*I/2) )
(Magma) I:=[2, 25]; [n le 2 select I[n] else 25*Self(n-1) +Self(n-2): n in [1..25]];
(Sage) [2*(-I)^n*chebyshev_T(n, 25*I/2) for n in (0..25)]
(GAP) a:=[2, 25];; for n in [3..25] do a[n]:=25*a[n-1]+a[n-2]; od; a;

Crossrefs

Lucas polynomials Lucas(n,m): A000032 (m=1), A002203 (m=2), A006497 (m=3), A014448 (m=4), A087130 (m=5), A085447 (m=6), A086902 (m=7), A086594 (m=8), A087798 (m=9), A086927 (m=10), A001946 (m=11), A086928 (m=12), A088316 (m=13), A090300 (m=14), A090301 (m=15), A090305 (m=16), A090306 (m=17), A090307 (m=18), A090308 (m=19), A090309 (m=20), A090310 (m=21), A090313 (m=22), A090314 (m=23), A090316 (m=24), this sequence (m=25).

Sequence in context: A121252 A322727 A090733 * A197084 A366038 A337153

Adjacent sequences: A330764 A330765 A330766 * A330768 A330769 A330770

Keyword

nonn,easy

Author

G. C. Greubel, Dec 29 2019

Status

approved