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A084232 RMS values associated with A084231. 6
1, 195, 37829, 7338631, 1423656585, 276182038859, 53577891882061, 10393834843080975, 2016350381665827089, 391161580208327374291, 75883330210033844785365, 14720974899166357560986519, 2855793247108063332986599321, 554009168964065120241839281755 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..436

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (194,-1).

FORMULA

a(n) = ((7+4*sqrt(3))^(2*n+1)-(7-4*sqrt(3))^(2*n+1))/(8*sqrt(3)).

a(n) = floor(((7*sqrt(3) + 12)/24)*(56*sqrt(3) + 97)^n).

a(n+2) = 194*a(n+1) - a(n).

G.f.: (1-x)/(1-194*x+x^2). - Philippe Deléham, Nov 18 2008

a(n)^2 = sum(i^2, i=1..A084231(n+1))/A084231(n+1). - Bruno Berselli, Oct 17 2012

EXAMPLE

a(1)=195 because 195 = sqrt(sum(k^2, k=1..337)/337) and 337=A84231(1).

CROSSREFS

Cf. A084231, A217855.

Sequence in context: A284960 A226105 A164130 * A145305 A174890 A077594

Adjacent sequences:  A084229 A084230 A084231 * A084233 A084234 A084235

KEYWORD

nonn,easy

AUTHOR

Ignacio Larrosa Cañestro, May 20 2003

EXTENSIONS

First formula simplified by Bruno Berselli, Oct 19 2012

STATUS

approved

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Last modified May 30 03:42 EDT 2017. Contains 287305 sequences.