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A322707 a(0)=0, a(1)=5 and a(n) = 22*a(n-1) - a(n-2) + 10 for n > 1. 2
0, 5, 120, 2645, 58080, 1275125, 27994680, 614607845, 13493377920, 296239706405, 6503780163000, 142786923879605, 3134808545188320, 68823001070263445, 1510971215000607480, 33172543728943101125, 728284990821747617280, 15989097254349504479045 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..700

Index entries for linear recurrences with constant coefficients, signature (23,-23,1).

FORMULA

sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(6) + sqrt(5))^n.

sqrt(a(n)+1) - sqrt(a(n)) = (sqrt(6) - sqrt(5))^n.

a(n) = 23*a(n-1) - 23*a(n-2) + a(n-3) for n > 2.

From Colin Barker, Dec 24 2018: (Start)

G.f.: 5*x*(1 + x) / ((1 - x)*(1 - 22*x + x^2)).

a(n) = ((11+2*sqrt(30))^(-n) * (-1+(11+2*sqrt(30))^n)^2) / 4.

(End)

EXAMPLE

(sqrt(6) + sqrt(5))^2 = 11 + 2*sqrt(30) = sqrt(121) + sqrt(120). So a(2) = 120.

PROG

(PARI) concat(0, Vec(5*x*(1 + x) / ((1 - x)*(1 - 22*x + x^2)) + O(x^20))) \\ Colin Barker, Dec 24 2018

CROSSREFS

Row 5 of A322699.

Cf. A188930 (sqrt(5)+sqrt(6)).

Sequence in context: A193328 A002008 A307350 * A160695 A158564 A252928

Adjacent sequences:  A322704 A322705 A322706 * A322708 A322709 A322710

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Dec 24 2018

STATUS

approved

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Last modified April 10 00:05 EDT 2020. Contains 333392 sequences. (Running on oeis4.)