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Search: id:A008937
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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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+0
15
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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; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = number of n-bit sequences that avoid 1100. - David Callan (callan(AT)stat.wisc.edu), Jul 19 2004
Row sums of Riordan array (1/(1-x), x(1+x+x^2)). - Paul Barry (pbarry(AT)wit.ie), Feb 16 2005
Diagonal sums of Riordan array (1/(1-x)^2,x(1+x)/(1-x)), A104698.
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REFERENCES
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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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FORMULA
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G.f.: x/(1-2x+x^4). 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
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MAPLE
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A008937 := proc(n) option remember; if n <= 3 then 2^n else 2*A008937(n-1)-A008937(n-4) fi; end;
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MATHEMATICA
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CoefficientList[Series[1/(1-2x+x^4), {x, 0, 40}], x]
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CROSSREFS
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a(n) = A018921(n-2) = A027084(n+1)+1.
Equals (1/2) [A000073(n+2) + A000073(n+4) - 1].
Row sums of A055216.
Adjacent sequences: A008934 A008935 A008936 this_sequence A008938 A008939 A008940
Sequence in context: A062065 A008936 A073769 this_sequence A128805 A049864 A118870
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KEYWORD
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nonn
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AUTHOR
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njas, Alejandro Teruel (teruel(AT)usb.ve)
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