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A047521
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Numbers that are congruent to {0, 7} mod 8.
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8
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0, 7, 8, 15, 16, 23, 24, 31, 32, 39, 40, 47, 48, 55, 56, 63, 64, 71, 72, 79, 80, 87, 88, 95, 96, 103, 104, 111, 112, 119, 120, 127, 128, 135, 136, 143, 144, 151, 152, 159, 160, 167, 168, 175, 176, 183, 184, 191, 192, 199, 200, 207, 208, 215, 216, 223, 224, 231, 232
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OFFSET
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1,2
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COMMENTS
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Except for 0, numbers whose binary reflected Gray code (A014550) ends with 00. - Amiram Eldar, May 17 2021
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LINKS
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Lars Pos, Met kleine stapjes grote sprongen make, Pythagoras 61-4. Solutions of returning to the origin after steps of increasing width 1,2,3,.. in the 4 directions on a square grid (in Dutch).
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FORMULA
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a(n) = 3*(-1)^n/2 - 5/2 + 4*n.
G.f.: x^2*(7+x) / ( (1+x)*(x-1)^2 ). (End)
Sum_{n>=2} (-1)^n/a(n) = log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8 - (sqrt(2)+1)*Pi/16. - Amiram Eldar, Dec 18 2021
E.g.f.: 1 + ((8*x -5)*exp(x) + 3*exp(-x))/2. David Lovler, Aug 22 2022
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MATHEMATICA
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{#, #+7}&/@(8*Range[0, 30])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 7, 8}, 60] (* Harvey P. Dale, Oct 30 2016 *)
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PROG
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(R)
kmax <- 10 # by choice
a <- c(0, 7)
for(k in 3:kmax) a <- c(a, a + 2^k)
a
(PARI) a(n) = 4*n - 5/2 + 3*(-1)^n/2; \\ David Lovler, Jul 25 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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