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

Author

Harvey P. Dale, Mar 23 2011

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A123270.

Programs

Mathematica

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

Formula

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

a(n) = 1/5 2^-n (-(5-3 Sqrt[5])^n (2+Sqrt[5])+(-2+Sqrt[5]) (5+3 Sqrt[5])^n)