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A091344 a(n) = 2*3^n-3*2^n+1. 3
0, 1, 7, 31, 115, 391, 1267, 3991, 12355, 37831, 115027, 348151, 1050595, 3164071, 9516787, 28599511, 85896835, 257887111, 774054547, 2322950071, 6970423075, 20914414951, 62749536307, 188261191831, 564808741315, 1694476555591 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Starting with offset 1 = binomial transform of A068193: (1, 6, 18, 42, 90,...) and double binomial transform of (1, 5, 7, 5, 7, 5,...). [From Gary W. Adamson, Jan 13 2009]

REFERENCES

Ballot, Christian and Luca, Florian, Prime factors of a^f(n)-1 with an irreducible polynomial f(x). New York J. Math. 12 (2006), 39-45 (electronic).

Ballot, Christian and Luca, Florian, Common prime factors of a^n-b and c^n-d. Unif. Distrib. Theory 2 (2007), no. 2, 19-34 (electronic).

LINKS

Table of n, a(n) for n=0..25.

Index to sequences with linear recurrences with constant coefficients, signature (6,-11,6).

FORMULA

a(n)=Sum(i!*i^2*Stirling2(n,i)*(-1)^(n-i), i=1,..,n)

a_n = 6a_{n-1} - 11a_{n-2} + 6a_{n-3}, g.f.: x(1+x)/(1-x)(2-x)(3-x)). - Christian Ballot via R. K. Guy, Jan 13 2009

a(n)=5*a(n-1)-6*a(n-2)+2  (a(0)=0, a(1)=1) [From Vincenzo Librandi, Nov 25 2010]

MAPLE

a:=n->sum((3^(n-j-1)-2^(n-2-j))*12, j=0..n): seq(a(n), n=-1..24); - Zerinvary Lajos, Feb 11 2007

with (combinat):a:=n->stirling2(n, 3)+stirling2(n+1, 3): seq(a(n), n=1..26); - Zerinvary Lajos, Oct 07 2007

MATHEMATICA

Table[Sum[i!i^2 StirlingS2[n, i](-1)^(n - i), {i, 1, n}], {n, 0, 30}]

Table[2*3^n-3*2^n+1, {n, 0, 30}] (* or *) LinearRecurrence[{6, -11, 6}, {0, 1, 7}, 30] (* Harvey P. Dale, Dec 31 2013 *)

CROSSREFS

A068293 [From Gary W. Adamson, Jan 13 2009]

Sequence in context: A097786 A197649 A006458 * A032197 A114289 A147597

Adjacent sequences:  A091341 A091342 A091343 * A091345 A091346 A091347

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Jan 01 2004

EXTENSIONS

Edited by N. J. A. Sloane, Jan 13 2009 at the suggestion of R. K. Guy. The concise definition was provided by Vladeta Jovovic, Jan 01 2004.

STATUS

approved

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Last modified November 27 23:10 EST 2014. Contains 250286 sequences.