A234018 -id:A234018 - cp's OEIS frontend

A233270 a(n) = A233271(n) - A179016(n).

0, 0, -1, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 0, 3, 3, 4, 3, 4, 3, 3, 0, 0, 4, 4, 5, 4, 6, 5, 5, 3, 5, 5, 6, 4, 5, 4, 4, 0, 0, 5, 8, 9, 10, 13, 13, 15, 16, 17, 18, 18, 17, 17, 19, 19, 17, 17, 18, 18, 17, 16, 15, 13, 13, 10, 9, 8, 5, 0, 0, 6, 9, 14, 17, 18, 20, 22, 21

Offset: 0

Antti Karttunen, Dec 14 2013

For all n>=2, a(1+A213710(n)) = n-2.
Except for a(2)=-1 (which seems to be the only negative term in the sequence), the sequences A218600 and A213710 give the positions of zeros.
Furthermore, each subrange [A213710(n)..A218600(n+1)] is palindromic. A233268 gives the middle points of those ranges, the sequence A234018 gives the values at those points, while A234019 gives the maximum term in that range in this sequence.

			This irregular table begins as:
0;
0;
-1;
0, 0;
0, 1, 0;
0, 2, 1, 2, 0;
0, 3, 3, 4, 3, 4, 3, 3, 0;
0, 4, 4, 5, 4, 6, 5, 5, 3, 5, 5, 6, 4, 5, 4, 4, 0;
...
After zero, each row n is A213709(n-1) elements long.

Antti Karttunen, Rows 0..16, flattened

Except for a(2)=-1 (which seems to be the only negative term in the sequence), the sequences A218600 and A213710 give the positions of zeros.

Cf. A080468, A179016, A233271, A233268, A233274, A234018, A234019, A234020.

(define (A233270 n) (- (A233271 n) (A179016 n)))

a(n) = A233271(n) - A179016(n).

a(A218602(n)) = a(n). [This is just a claim that each row is palindrome]

A233268 The middle point of row n in binary beanstalk related sequences A179016, A218602, A218616, A233270, A233271.

Original entry on oeis.org

1, 2, 3, 6, 10, 17, 30, 53, 95, 171, 310, 564, 1036, 1918, 3574, 6691, 12566, 23653, 44610, 84309, 159698, 303253, 577352, 1102121, 2109448, 4047967, 7787277, 15015347, 29011671, 56150867, 108825599, 211127246, 409886210, 796134319, 1546848744, 3006198333, 5843799964

Offset: 1

Antti Karttunen, Dec 29 2013

nonn

a(n) points to the center of each palindromic row/subrange of A233270, and to the lower position nearest to the center, if the length of range is even.

For all n, A218602(a(n)) = a(n) + (1-A000035(A213709(n-1))).

Cf. A213709, A213710, A218600, A234018, A234019, A234020.

Cf. also A179016, A218602, A218616, A233270, A233271.

a(n) = floor((A213710(n-1) + A218600(n)) / 2).

a(n) = A218600(n-1) + ceiling((A213709(n-1)/2)).

A234020 Offsets from the middle point of each row of A233270 to the nearest point containing a maximum value of that range.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 3, 0, 5, 0, 0, 33, 72, 140, 267, 502, 954, 1771, 3355

Offset: 1

Antti Karttunen, Dec 29 2013

nonn

Please see the graph of A233270. Iff a(n)=0, A234018(n) = A234019(n).

Seems to grow faster than A233274. Is the ratio a(n)/A233274(n) converging to some limit?

Cf. A233268, A233270, A234018, A234019, A233274.

(define (A234020 n) (let ((middle (A233268 n))) (let loop ((i middle) (m 0) (maxp middle)) (cond ((zero? (A233270 i)) (- middle maxp)) ((> (abs (A233270 i)) m) (loop (- i 1) (abs (A233270 i)) i)) (else (loop (- i 1) m maxp))))))

A234019 Maximum values occurring in each row of A233270: a(n) = A233270(A233268(n) - A234020(n)).

Original entry on oeis.org

0, -1, 0, 1, 2, 4, 6, 19, 38, 67, 127, 234, 419, 745, 1378, 2678, 5311, 10470, 20333

Offset: 1

Antti Karttunen, Dec 29 2013

sign

Please see the graph of A233270.

Cf. A233268, A233270, A234018, A234020.

a(n) = A233270(A233268(n) - A234020(n)).

cp's OEIS Frontend

A233270 a(n) = A233271(n) - A179016(n).

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A233268 The middle point of row n in binary beanstalk related sequences A179016, A218602, A218616, A233270, A233271.

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A234020 Offsets from the middle point of each row of A233270 to the nearest point containing a maximum value of that range.

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A234019 Maximum values occurring in each row of A233270: a(n) = A233270(A233268(n) - A234020(n)).

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