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A322708 a(0)=0, a(1)=6 and a(n) = 26*a(n-1) - a(n-2) + 12 for n > 1. 2
0, 6, 168, 4374, 113568, 2948406, 76545000, 1987221606, 51591216768, 1339384414374, 34772403556968, 902743108066806, 23436548406180000, 608447515452613206, 15796198853361763368, 410092722671953234374, 10646614590617422330368, 276401886633381027355206 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (27,-27,1).

FORMULA

sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(7) + sqrt(6))^n.

sqrt(a(n)+1) - sqrt(a(n)) = (sqrt(7) - sqrt(6))^n.

a(n) = 27*a(n-1) - 27*a(n-2) + a(n-3) for n > 2.

From Colin Barker, Dec 24 2018: (Start)

G.f.: 6*x*(1 + x) / ((1 - x)*(1 - 26*x + x^2)).

a(n) = ((13+2*sqrt(42))^(-n) *  (-1+(13+2*sqrt(42))^n)^2) / 4.

(End)

EXAMPLE

(sqrt(7) + sqrt(6))^2 = 13 + 2*sqrt(42) = sqrt(169) + sqrt(168). So a(2) = 168.

PROG

(PARI) concat(0, Vec(6*x*(1 + x) / ((1 - x)*(1 - 26*x + x^2)) + O(x^20))) \\ Colin Barker, Dec 24 2018

CROSSREFS

Row 6 of A322699.

Sequence in context: A143534 A104729 A106661 * A181013 A003720 A306837

Adjacent sequences:  A322705 A322706 A322707 * A322709 A322710 A322711

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Dec 24 2018

STATUS

approved

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)