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Search: id:A026383
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| A026383 |
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T(n,0) + T(n,1) + ... + T(n,n), where T is the array in A026374. |
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9
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| 1, 2, 5, 10, 25, 50, 125, 250, 625, 1250, 3125, 6250, 15625, 31250, 78125, 156250, 390625, 781250, 1953125, 3906250, 9765625, 19531250, 48828125, 97656250, 244140625, 488281250, 1220703125, 2441406250, 6103515625, 12207031250
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of lattice paths from (0,0) to the line x=n using steps U=(1,1), D=(1,-1) and, at levels ...-4,-2,0,2,4,..., also H=(2,0). Example: a(2)=5 because we have the following paths from (0,0) to the line x=2: UU, UD, H, DU, and DD. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 25 2004
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FORMULA
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Also number of integer strings s(0), ...s(n) such that s(0) = 0, where, for 1<=i<=n, s(i) is even if i is even and |s(i)-s(i-1)|<=1.
a(2n)=5^n, a(2n+1)=2*5^n. G.f.=(1+2z)/(1-5z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 25 2004
Second inverse binomial transform of Fib(3n+3)/2. a(n)=5^(n/2)((1/2+1/sqrt(5))+(1/2-1/sqrt(5))(-1)^n) - Paul Barry (pbarry(AT)wit.ie), Apr 16 2004
a(n)=a(n-1)+2a(n-2)+5^floor((n-2)/2); a(n)=sum{k=0..floor(n/2), binomial(floor(n/2), k)2^(n-2k) }. - Paul Barry (pbarry(AT)wit.ie), Jul 14 2004
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CROSSREFS
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Cf. A026374.
Sequence in context: A109616 A018262 A018356 this_sequence A002094 A115725 A079572
Adjacent sequences: A026380 A026381 A026382 this_sequence A026384 A026385 A026386
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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