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Irregular table T(n, k), n > 0, k = 1..A000010(n); the n-th row lists the numbers k such that fusc(k) + fusc(k+1) = n, where "fusc" is Stern's diatomic series (A002487).
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%I #11 Dec 16 2022 11:52:18

%S 0,1,2,3,4,7,5,6,8,15,16,31,9,11,12,14,32,63,10,13,64,127,17,23,24,30,

%T 128,255,19,28,256,511,18,20,27,29,33,47,48,62,512,1023,22,25,1024,

%U 2047,21,26,35,39,56,60,65,95,96,126,2048,4095,34,40,55,61,4096,8191

%N Irregular table T(n, k), n > 0, k = 1..A000010(n); the n-th row lists the numbers k such that fusc(k) + fusc(k+1) = n, where "fusc" is Stern's diatomic series (A002487).

%C Every nonnegative integer m appears in this sequence (in row fusc(m) + fusc(m+1)).

%H Rémy Sigrist, <a href="/A359051/b359051.txt">Table of n, a(n) for n = 1..5022</a>

%H Rémy Sigrist, <a href="/A359051/a359051.gp.txt">PARI program</a>

%H <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>

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

%F T(n, 1) = A359050(n).

%F T(n, A000010(n)) = 2^(n-1) - 1.

%e Array T(n, k) begins:

%e 0,

%e 1,

%e 2, 3,

%e 4, 7,

%e 5, 6, 8, 15,

%e 16, 31,

%e 9, 11, 12, 14, 32, 63,

%e 10, 13, 64, 127,

%e 17, 23, 24, 30, 128, 255,

%e 19, 28, 256, 511,

%e 18, 20, 27, 29, 33, 47, 48, 62, 512, 1023,

%e 22, 25, 1024, 2047,

%e ...

%o (PARI) See Links section.

%Y Cf. A000010, A002487, A359050.

%K nonn,tabf

%O 1,3

%A _Rémy Sigrist_, Dec 14 2022