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A125145
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a(n) = 3a(n-1) + 3a(n-2). a(0) = 1, a(1) = 4.
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16
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1, 4, 15, 57, 216, 819, 3105, 11772, 44631, 169209, 641520, 2432187, 9221121, 34959924, 132543135, 502509177, 1905156936, 7222998339, 27384465825, 103822392492, 393620574951, 1492328902329, 5657848431840, 21450532002507
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of aa-avoiding words of length n on the alphabet {a,b,c,d}.
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2010: (Start)
Equals row 3 of the array shown in A180165, the INVERT transform of A028859
and the INVERTi transform of A086347. (End)
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Joerg Arndt, Fxtbook
Tanya Khovanova, Recursive Sequences
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| G.f.=(1+z)/(1-3z-3z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007
a(n) = (5*sqrt(21)/42 + 1/2)*(3/2 + sqrt(21)/2))^(n-1) + (-5*sqrt(21)/42 + 1/2)*(3/2 - sqrt(21)/2))^(n-1). - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 20 2008
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MAPLE
| a[0]:=1: a[1]:=4: for n from 2 to 27 do a[n]:=3*a[n-1]+3*a[n-2] od: seq(a[n], n=0..27); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007
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PROG
| #include <iostream.h> #include <stdlib.h> #include <math.h> int main(int argc, char *argv[]) { int i; // counter for for loop double j; // for (i=1; i < 12; i++) // change 9 to whatever number you want if desired { j = ( 5.0*sqrt(21.0)/42 + 1.0/2.0)*pow((3.0/2.0 + sqrt(21)/2), (i-1))+ (-5.0*sqrt(21.0)/42 + 1.0/2.0)*pow((3.0/2.0 - sqrt(21)/2), (i-1)) ; // cout << i << ' ' << j << " "; } return EXIT_SUCCESS; } - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 20 2008
(Haskell)
a125145 n = a125145_list !! n
a125145_list =
1 : 4 : map (* 3) (zipWith (+) a125145_list (tail a125145_list))
-- Reinhard Zumkeller, Oct 15 2011
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CROSSREFS
| Cf. A028859 = a(n+2) = 2 a(n+1) + 2 a(n); A086347 = On a 3 X 3 board, number of n-move routes of chess king ending at a given side cell. a(n) = 4a(n-1) + 4a(n-2).
Cf. A128235.
Cf. A180165, A028859, A086347 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 14 2010]
Cf. A002605, A026150, A030195, A080040, A083337, A106435, A108898.
Sequence in context: A174958 A077823 A047108 * A095930 A026850 A109642
Adjacent sequences: A125142 A125143 A125144 * A125146 A125147 A125148
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KEYWORD
| nonn
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AUTHOR
| Tanya Khovanova (tanyakh(AT)yahoo.com), Jan 11 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007
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