

A104743


Numbers m = n + 3^n such that the equation x = 3^(mx) has solution x = 3^n.


15



1, 4, 11, 30, 85, 248, 735, 2194, 6569, 19692, 59059, 177158, 531453, 1594336, 4782983, 14348922, 43046737, 129140180, 387420507, 1162261486, 3486784421, 10460353224, 31381059631, 94143178850, 282429536505, 847288609468
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OFFSET

0,2


COMMENTS

This sequence also describes the total number of moves solving (nonoptimally) the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] precolored Magnetic Tower of Hanoi puzzle (see the "CROSSREFS" in A183121). For other Magnetic Tower of Hanoi related sequences, cf. A183111  A183125.
The allowable number of dimensions in supersymmetric geometries, according to Thad Roberts.  Howard A. Landman, Jan 09 2013
Form an infinite array with m(0,k) = 2*k+1 and m(n,k) = Sum_{r=0..n1} m(r,k) + Sum_{c=0..k1} m(n,c), being the sum of the terms above m(n,k) plus those terms to the left of m(n,k). The first row is A005408. The second row is A033484. The first column is A011782. The sum of the terms in the nth antidiagonal is a(n).  J. M. Bergot, Jun 07 2013


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Uri Levy, The Magnetic Tower of Hanoi, arXiv:1003.0225 [math.CO], 2010.
Thad Roberts, Quantum Space Theory.
Index entries for linear recurrences with constant coefficients, signature (5,7,3).


FORMULA

a(n) = n + 3^n.
From Colin Barker, Jan 25 2012: (Start)
a(n) = 5*a(n1)  7*a(n2) + 3*a(n3).
G.f.: (1+x)*(12*x) / ((13*x)*(1x)^2). (End)
E.g.f.: x*exp(x) + exp(3*x).  G. C. Greubel, May 21 2019


MAPLE

g:=1/(13*z): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)+n, n=0..31); # Zerinvary Lajos, Jan 09 2009


MATHEMATICA

Table[3^n +n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Jan 18 2009, modified by G. C. Greubel, May 21 2019 *)
LinearRecurrence[{5, 7, 3}, {1, 4, 11}, 30] (* Harvey P. Dale, Aug 01 2020 *)


PROG

(PARI) {a(n) = 3^n + n}; \\ G. C. Greubel, May 21 2019
(MAGMA) [3^n +n: n in [0..40]]; // G. C. Greubel, May 21 2019
(Sage) [3^n +n for n in (0..40)] # G. C. Greubel, May 21 2019
(GAP) List([0..40], n> 3^n +n ) # G. C. Greubel, May 21 2019


CROSSREFS

Cf. A103537.
Sequence in context: A183123 A183116 A183121 * A165993 A192312 A004080
Adjacent sequences: A104740 A104741 A104742 * A104744 A104745 A104746


KEYWORD

nonn,easy


AUTHOR

Zak Seidov, Mar 23 2005


EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, Jan 18 2009


STATUS

approved



