Search: a284173 -id:a284173
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1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 3, 4, 5, 4, 5, 5, 5, 6, 6, 6, 6, 8, 6, 8, 8, 8, 8, 8, 10, 8, 9, 10, 10, 10, 11, 11, 10, 11, 11, 11, 12, 12, 12, 12, 12, 16, 10, 14, 14, 12, 14, 16, 14, 14, 16, 14, 16, 16, 16, 16, 20, 16, 17, 21, 16, 17, 19, 20, 20, 21, 21, 20, 19, 19, 22, 19, 21, 21, 22, 22, 22, 23, 21, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 32, 17, 32
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OFFSET
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1,5
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COMMENTS
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For n >= 2, a(n) gives the left hand summand for the term q(n+1) of Hofstadter Q-sequence (A005185): q(1) = q(2) = 1; q(n) = q(n-q(n-1)) + q(n-q(n-2)) for n > 2.
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LINKS
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FORMULA
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MATHEMATICA
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a[1] = a[2] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[n - a[n - 2]]; Table[a[n + 1 - a[n]], {n, 97}] (* Michael De Vlieger, Mar 22 2017 *)
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PROG
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(PARI) q(n) = if(n<3, 1, q(n - q(n - 1)) + q(n - q(n - 2)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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1, 2, 3, 4, 6, 8, 10, 13, 16, 19, 23, 26, 30, 35, 39, 44, 49, 54, 60, 66, 72, 78, 86, 92, 100, 108, 116, 124, 132, 142, 150, 159, 169, 179, 189, 200, 211, 221, 232, 243, 254, 266, 278, 290, 302, 314, 330, 340, 354, 368, 380, 394, 410, 424, 438, 454, 468, 484, 500, 516, 532, 552, 568, 585, 606, 622, 639, 658, 678, 698, 719, 740
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OFFSET
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1,2
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LINKS
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FORMULA
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a(1) = 1, for > 1, a(n) = A283467(n) + a(n-1).
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MATHEMATICA
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a[1] = a[2] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[n - a[n - 2]]; Accumulate@ Table[a[n + 1 - a[n]], {n, 72}] (* Michael De Vlieger, Mar 22 2017 *)
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PROG
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(Scheme)
;; Code for A005185 given under that entry.
;; With memoization-macro definec:
;; As an explicit sum (slower):
;; Implements sum_{i=lowlim..uplim} intfun(i)
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))
(PARI) a(n) = if(n<3, 1, a(n - a(n - 1)) + a(n - a(n - 2)));
for(n=1, 72, print1(sum(k=1, n, a(k + 1 - a(k))), ", ")) \\ Indranil Ghosh, Mar 22 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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