A188168 a(0) = a(1) = 1; a(n) = 5*a(n-1) + 5*a(n-2).

1, 1, 10, 55, 325, 1900, 11125, 65125, 381250, 2231875, 13065625, 76487500, 447765625, 2621265625, 15345156250, 89832109375, 525886328125, 3078592187500, 18022392578125, 105504923828125, 617636582031250, 3615707529296875, 21166720556640625

Offset

0,3

Comments

First differences give {0,9,45,270,1575,9225,54000,316125,1850625,10833750,63421875,371278125, ...}.

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (5,5).

Formula

G.f.: (4*x-1)/(5*x^2+5*x-1).

a(n) = (1/10)*2^-n*((5+sqrt(5))*(5-3*sqrt(5))^n+(5-sqrt(5))*(5+3*sqrt(5))^n).

Mathematica

Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{5, 5}, #]}]&, {1, 1}, 40]][[1]]
LinearRecurrence[{5, 5}, {1, 1}, 30] (* Harvey P. Dale, Nov 19 2024 *)

Prog

(PARI) lista(nn) = {my(va=vector(nn+2)); va[1]=va[2]=1; for(n=1, nn, va[n+2]=5*va[n]+ 5*va[n+1]; ); va; } \\ Bruce Nye, Mar 18 2026

Crossrefs

Cf. A123270.

Sequence in context: A253002 A357668 A316109 * A199413 A054629 A290359

Adjacent sequences: A188165 A188166 A188167 * A188169 A188170 A188171

Keyword

nonn,easy

Author

Harvey P. Dale, Mar 23 2011

Status

approved