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f[n_] := NestWhileList[# - (If[First@ # > 0, 1, Length[First@ Split@ #] + 1] &@ SquaresR[Range@ 4, #]) &, n^2, # != 0 &]; t = Table[Table[n, {Length[#] - 1 &@ NestWhileList[# - (If[First@ # > 0, 1, Length[First@ Split@ #] + 1] &@ SquaresR[Range@ 4, #]) &, ((n + 1)^2) - 1, # != (n^2) - 1 &]}], {n, 20}] // Flatten ; {0}~Join~Table[Length@ f@ t[[n]] - 1 + Length@ f[t[[n]] + 1] - n - 2, {n, 81}] (* Michael De Vlieger, Sep 08 2016 *)

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t = Table[Table[n, {Length[#] - 1 &@ NestWhileList[# - (If[First@ # > 0, 1, Length[First@ Split@ #] + 1] &@ SquaresR[Range@ 4, #]) &, ((n + 1)^2) - 1, # != (n^2) - 1 &]}], {n, 20}] // Flatten ; {0}~Join~Table[Length@ f@ t[[n]] - 1 + Length@ f[t[[n]] + 1] - n - 2, {n, 81}] (* Michael De Vlieger, Sep 08 2016 *)

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Antti Karttunen, <a href="/A276572/b276572.txt">Table of n, a(n) for n = 0..10028</a>

<a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

allocated for Antti KarttunenSimple self-inverse permutation of natural numbers: after a(0)=0, list each block of A260734(n) numbers in reverse order, from A260732(n) to A260733(1+n).

0, 1, 3, 2, 5, 4, 9, 8, 7, 6, 13, 12, 11, 10, 18, 17, 16, 15, 14, 23, 22, 21, 20, 19, 30, 29, 28, 27, 26, 25, 24, 37, 36, 35, 34, 33, 32, 31, 44, 43, 42, 41, 40, 39, 38, 52, 51, 50, 49, 48, 47, 46, 45, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 71, 70, 69, 68, 67, 66, 65, 64, 63, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72

0,3

Maps between A276573 and A276574.

a(0) = 0; for n >= 1, a(n) = (A260733(1+A276571(n))-n)+A260732(A276571(n)).

(Scheme) (define (A276572 n) (if (zero? n) n (+ (- (A260733 (+ 1 (A276571 n))) n) (A260732 (A276571 n)))))

Cf. A260732, A260733, A260734, A276573, A276574.

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nonn

Antti Karttunen, Sep 07 2016

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allocated for Antti Karttunen

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