Revision History for A325664
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#16 by Peter Luschny at Tue Jun 18 13:36:22 EDT 2019
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#15 by Peter Luschny at Tue Jun 18 13:35:06 EDT 2019
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| COMMENTS
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Guide to related sequences:
A325664, r = sqrt(2)
A325665, r = -sqrt(2)
A325666, r = sqrt(3)
A325667, r = -sqrt(3)
A325668, r = sqrt(5)
A325669, r = -sqrt(5)
A325670, r = sqrt(6)
A325671, r = -sqrt(6)
A325672, r = sqrt(7)
A325673, r = -sqrt(7)
A325674, r = sqrt(8)
A325675, r = -sqrt(8)
A325729, r = sqrt(1/2)
A325730, r = sqrt(1/3)
A325731, r = sqrt(2/3)
A325732, r = sqrt(3/4)
A325733, r = 1/2 + sqrt(2)
A325734, r = e
A325735, r = -e
A325736, r = 2e
A325737, r = 3e
A325738, r = e/2
A325739, r = Pi
A325740, r = 2Pi
A325741, r = Pi/2
A325742, r = Pi/3
A325743, r = Pi/4
A325744, r = Pi/6
A325745, r = tau = golden ratio = (1 + sqrt(5))/2
A325746, r = -tau
A325747, r = tau^2 = 1 + tau
A325748, r = 1/e
A325749, r = e/(e-1)
A325750, r = (1+sqrt(3))/2
A325751, r = log 2
A325752, r = log 3
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| EXAMPLE
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1st difference sequence: : 1, , 1, , 2, , 1, , 2, , 1, , 1, , 2, , 1, , 2, , 1, , 1, , 2, 1, ..., ...
2nd difference sequence: : 0, , 1, -1, , 1, -1, , 0, , 1, -1, , 1, -1, , 0, , 1, -1, ...
3rd difference sequence: : 1, -2, , 2, -2, , 1, , 1, -2, , 2, -2, , 1, , 1, -2, , 2, ...
4th difference sequence: -3, , 4, -4, , 3, , 0, -3, , 4, -4, , 3, , 0, -3, , 4, -4, ...
5th difference sequence: : 7, -8, , 7, -3, -3, , 7, -8, , 7, -3, -3, , 7, -8, , 7, ...
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| MAPLE
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L:= L[2..-1]-L[1..-2];
Res:= Res, L[1];
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| CROSSREFS
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Cf. A001951, A325665.
Guide to related sequences:
A325664, r = sqrt(2)
A325665, r = -sqrt(2)
A325666, r = sqrt(3)
A325667, r = -sqrt(3)
A325668, r = sqrt(5)
A325669, r = -sqrt(5)
A325670, r = sqrt(6)
A325671, r = -sqrt(6)
A325672, r = sqrt(7)
A325673, r = -sqrt(7)
A325674, r = sqrt(8)
A325675, r = -sqrt(8)
A325729, r = sqrt(1/2)
A325730, r = sqrt(1/3)
A325731, r = sqrt(2/3)
A325732, r = sqrt(3/4)
A325733, r = 1/2 + sqrt(2)
A325734, r = e
A325735, r = -e
A325736, r = 2e
A325737, r = 3e
A325738, r = e/2
A325739, r = Pi
A325740, r = 2Pi
A325741, r = Pi/2
A325742, r = Pi/3
A325743, r = Pi/4
A325744, r = Pi/6
A325745, r = tau = golden ratio = (1 + sqrt(5))/2
A325746, r = -tau
A325747, r = tau^2 = 1 + tau
A325748, r = 1/e
A325749, r = e/(e-1)
A325750, r = (1+sqrt(3))/2
A325751, r = log 2
A325752, r = log 3
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| STATUS
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proposed
editing
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#14 by Robert Israel at Tue Jun 04 22:57:28 EDT 2019
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Discussion
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| Wed Jun 05
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| Felix Fröhlich: Doesn't this comment rather belong in crossrefs section?
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#13 by Robert Israel at Tue Jun 04 22:57:21 EDT 2019
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| FORMULA
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From Robert Israel, Jun 04 2019: (Start)
a(n) = Sum_{0<=k<=n} (-1)^(n-k)*binomial(n,k)*A001951(k).
G.f.: g(x) = (1+x)^(-1)*h(x/(1+x)) where h is the G.f. of A001951. (End)
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| MAPLE
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N:= 50: # for a(1)..a(N)
L:= [seq(floor(sqrt(2)*n), n=0..N)]: Res:= NULL:
for i from 1 to N do
L:= L[2..-1]-L[1..-2];
Res:= Res, L[1];
od:
Res; # Robert Israel, Jun 04 2019
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| STATUS
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proposed
editing
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#12 by Jon E. Schoenfield at Wed May 22 22:41:27 EDT 2019
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#11 by Jon E. Schoenfield at Wed May 22 22:41:24 EDT 2019
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| COMMENTS
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A325664, , r = sqrt(2)
A325667, , r = -sqrt(3)
A325668, , r = sqrt(5)
A325669, , r = -sqrt(5)
A325670, , r = sqrt(6)
A325671, , r = -sqrt(6)
A325672, , r = sqrt(7)
A325673, , r = -sqrt(7)
A325674, , r = sqrt(8)
A325675, , r = -sqrt(8)
A325746, r = - = -tau
A325748, r= = 1/e
A325749, r= = e/(e-1)
A325750, r= ( = (1+sqrt(3))/2
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| STATUS
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proposed
editing
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#10 by Clark Kimberling at Wed May 22 09:48:51 EDT 2019
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#9 by Clark Kimberling at Wed May 22 09:39:38 EDT 2019
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| NAME
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First term of n-th difference sequence of { (floor[k*r]}, ]), r = sqrt(2), k >= 0.
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| COMMENTS
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Guide to related sequences:
A325664, r = sqrt(2)
A325665, r = -sqrt(2)
A325666, r = sqrt(3)
A325667, r = -sqrt(3)
A325668, r = sqrt(5)
A325669, r = -sqrt(5)
A325670, r = sqrt(6)
A325671, r = -sqrt(6)
A325672, r = sqrt(7)
A325673, r = -sqrt(7)
A325674, r = sqrt(8)
A325675, r = -sqrt(8)
A325729, r = sqrt(1/2)
A325730, r = sqrt(1/3)
A325731, r = sqrt(2/3)
A325732, r = sqrt(3/4)
A325733, r = 1/2 + sqrt(2)
A325734, r = e
A325735, r = -e
A325736, r = 2e
A325737, r = 3e
A325738, r = e/2
A325739, r = Pi
A325740, r = 2Pi
A325741, r = Pi/2
A325742, r = Pi/3
A325743, r = Pi/4
A325744, r = Pi/6
A325745, r = tau = golden ratio = (1 + sqrt(5))/2
A325746, r = - tau
A325747, r = tau^2 = 1 + tau
A325748, r= 1/e
A325749, r= e/(e-1)
A325750, r= (1+sqrt(3))/2
A325751, r = log 2
A325752, r = log 3
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| MATHEMATICA
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Table[First[Differences[Table[Floor[Sqrt[2]*n], {n, 0, 3050}], n]], {n, 01, 50}]
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| STATUS
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approved
editing
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#8 by Sean A. Irvine at Sun May 19 21:29:20 EDT 2019
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#7 by Clark Kimberling at Sun May 19 21:02:02 EDT 2019
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