A188168 - OEIS

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

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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.: (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)

MATHEMATICA

Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{5, 5}, #]}]&, {1, 1}, 40]][[1]]

LinearRecurrence[{5, 5}, {1, 1}, 30] (* Harvey P. Dale, Nov 19 2024 *)

CROSSREFS

Cf. A123270.

Sequence in context: A253002 A357668 A316109 * A199413 A054629 A290359

Adjacent sequences: A188165 A188166 A188167 * A188169 A188170 A188171

KEYWORD

nonn,easy,changed

AUTHOR

Harvey P. Dale, Mar 23 2011

STATUS

approved