A094782 -id:A094782 - cp's OEIS frontend

A094781 Array T(i,j), i>=1, j >= 1, forming a two-dimensional version of A090822, read by antidiagonals.

1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 3, 3, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 3, 2, 2, 3, 1, 3, 2, 2, 3, 1, 3, 3, 3, 2, 2, 3, 3, 3, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 3, 2, 1, 2, 3, 1, 2, 2, 1

Offset: 1

N. J. A. Sloane, Jun 12 2004

T(1,i) = T(i,1) = A090822(i). For i and j > 1, T(i,j) = max {k1, k2}, where k1 = curling number of (T(i,1), T(i,2)...,T(i,j-1)), k2 = curling number of (T(1,j), T(2,j)...,T(i-1,j)).

The curling number of a finite string S = (s(1),...,s(n)) is the largest integer k such that S can be written as xy^k for strings x and y (where y has positive length).

			Array begins:
1 1 2 1 1 2 2 2 3 1 1 2 1 1 2 2 2 3 2 1 ... (A090822)
1 1 2 1 1 2 2 2 3 1 1 2 1 1 2 2 2 3 2 1 ... (A090822)
2 2 2 3 2 2 2 3 2 2 2 3 3 2 ... (A091787)
1 1 3 1 1 3 3 2 1 1 2 1 1 2 ... (A094782)
1 1 2 1 1 2 2 2 3 1 2 1 1 2 ... (A094839)
2 2 2 3 2 1 1 2 1 2 3 2 2 3 ...
2 2 2 3 2 1 1 3 1 2 ...

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
Index entries for sequences related to Gijswijt's sequence

Cf. A090822, A091787, A094782.

A094839 5th row of array in A094781.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 2, 1, 1, 2, 1, 2, 2, 2, 3, 1, 1, 2, 1, 2, 2, 2, 3, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 4, 1, 1, 2, 2, 4, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 2, 2, 2, 3, 1, 1, 2, 2, 2, 3, 1, 2, 1, 4, 1, 1, 2, 4, 1, 1, 2, 2, 4, 1, 2, 1, 1, 2, 1, 2, 2

Offset: 1

N. J. A. Sloane, Jun 12 2004

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.
F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].
Index entries for sequences related to Gijswijt's sequence

Cf. A090822, A091787, A094781, A094782.

More terms from David Wasserman, Jun 27 2007

A144646 a(n) = Bell(n) - 2^n + n.

Original entry on oeis.org

0, 0, 0, 0, 3, 25, 145, 756, 3892, 20644, 114961, 676533, 4209513, 27636258, 190882952, 1382925792, 10480076627, 82864738749, 682076544033, 5832741680788, 51724157186816, 474869814059620, 4506715734253041, 44152005846695761, 445958869278028097

Offset: 0

Jean-Yves Tallet and N. J. A. Sloane, Jan 26 2009

nonn

Number of partitions of an n-set having more than one block of size > 1. - Peter Luschny, Apr 10 2011

			a(5) = 25 = card({25|134, 35|124, 125|34, 345|12, 45|123, 235|14, 15|234, 145|23, 135|24, 245|13, 25|4|13, 35|4|12, 45|3|12, 5|24|13, 5|12|34, 1|35|24, 35|2|14, 25|3|14, 5|14|23, 1|45|23, 15|4|23, 45|2|13, 15|3|24, 15|2|34, 1|25|34}). - _Peter Luschny_, Apr 10 2011

Amiram Eldar, Table of n, a(n) for n = 0..576

Cf. A000110, A094782.

[Bell(n) -2^n +n: n in [0..30]]; // G. C. Greubel, Oct 12 2023

Table[BellB[n] - 2^n + n, {n, 0, 24}] (* Amiram Eldar, Nov 23 2019 *)

[bell_number(n) - 2^n +n for n in range(31)] # G. C. Greubel, Oct 12 2023

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A094781 Array T(i,j), i>=1, j >= 1, forming a two-dimensional version of A090822, read by antidiagonals.

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A094839 5th row of array in A094781.

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A144646 a(n) = Bell(n) - 2^n + n.

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