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A008937
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a(n) = Sum T(k), k=0,..,n, where T(n) are the tribonacci numbers A000073.
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27
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0, 1, 2, 4, 8, 15, 28, 52, 96, 177, 326, 600, 1104, 2031, 3736, 6872, 12640, 23249, 42762, 78652, 144664, 266079, 489396, 900140, 1655616, 3045153, 5600910, 10301680, 18947744, 34850335, 64099760, 117897840, 216847936, 398845537
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = number of n-bit sequences that avoid 1100. - David Callan, Jul 19 2004
Row sums of Riordan array (1/(1-x), x(1+x+x^2)). - Paul Barry, Feb 16 2005
Diagonal sums of Riordan array (1/(1-x)^2,x(1+x)/(1-x)), A104698.
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REFERENCES
| A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 41.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index to sequences with linear recurrences with constant coefficients, signature (2,0,0,-1)
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FORMULA
| G.f.: x/((x-1)*(x^3+x^2+x-1)). Recurrence a(n)=2a(n-1)-a(n-4), a(0)=0, a(1)=1, a(2)=2, a(3)=4. - Mario Catalani (mario.catalani(AT)unito.it), Aug 09 2002
a(n) = 1 + a(n-1) + a(n-2) + a(n-3). E.g. a(11) = 1 +600 + 326 + 177 = 1104. - Philippe LALLOUET (philip.lallouet(AT)orange.fr), Oct 29 2007
a(n) = term (4,1) in the 4x4 matrix [1,1,0,0; 1,0,1,0; 1,0,0,0; 1,0,0,1]^n. - Alois P. Heinz, Jul 24 2008
a(n) = -A077908(-n-3). - Alois P. Heinz, Jul 24 2008
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MAPLE
| A008937 := proc(n) option remember; if n <= 3 then 2^n else 2*procname(n-1)-procname(n-4) fi; end;
a:= n-> (Matrix ([[1, 1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 0], [1, 0, 0, 1]])^n)[4, 1]: seq (a(n), n=0..50); # Alois P. Heinz, Jul 24 2008
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MATHEMATICA
| CoefficientList[Series[1/(1-2x+x^4), {x, 0, 40}], x]
a=b=c=0; Table[d=a+b+c+1; a=b; b=c; c=d, {n, 0, 5!}] [From Vladimir Orlovsky, May 18 2010]
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PROG
| (MAGMA) [ n eq 1 select 0 else n eq 2 select 1 else n eq 3 select 2 else n eq 4 select 4 else 2*Self(n-1)-Self(n-4): n in [1..40] ]; // Vincenzo Librandi, Aug 21 2011
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CROSSREFS
| a(n) = A018921(n-2) = A027084(n+1)+1.
Equals (1/2) [A000073(n+2) + A000073(n+4) - 1].
Row sums of A055216.
Sequence in context: A062065 A008936 A073769 * A128805 A141018 A049864
Adjacent sequences: A008934 A008935 A008936 * A008938 A008939 A008940
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Alejandro Teruel (teruel(AT)usb.ve)
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