A255765 -id:A255765 - cp's OEIS frontend

A255741 Square array read by antidiagonals upwards: T(n,k), n>=1, k>=1, in which row n lists the partial sums of the n-th row of the square array of A255740.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 3, 1, 1, 5, 7, 7, 4, 1, 1, 6, 9, 13, 9, 4, 1, 1, 7, 11, 21, 16, 11, 4, 1, 1, 8, 13, 31, 25, 22, 13, 4, 1, 1, 9, 15, 43, 36, 37, 28, 15, 5, 1, 1, 10, 17, 57, 49, 56, 49, 40, 17, 5, 1, 1, 11, 19, 73, 64, 79, 76, 85, 43, 19, 5, 1, 1, 12, 21, 91, 81, 106, 109, 156, 89, 49, 21, 5, 1

Offset: 1

Omar E. Pol, Mar 05 2015

			The corner of the square array with the first 15 terms of the first 12 rows looks like this:
-------------------------------------------------------------------------
A000012: 1, 1, 1,  1,  1,  1,  1,   1,   1,   1,   1,   1,   1,   1,   1
A070941: 1, 2, 3,  3,  4,  4,  4,   4,   5,   5,   5,   5,   5,   5,   5
A005408: 1, 3, 5,  7,  9, 11, 13,  15,  17,  19,  21,  23,  25,  27,  29
A151788: 1, 4, 7, 13, 16, 22, 28,  40,  43,  49,  55,  67,  73,  85,  97
A147562: 1, 5, 9, 21, 25, 37, 49,  85,  89, 101, 113, 149, 161, 197, 233
A151790: 1, 6,11, 31, 36, 56, 76, 156, 161, 181, 201, 281, 301, 381, 461
A151781: 1, 7,13, 43, 49, 79,109, 259, 265, 295, 325, 475, 505, 655, 805
A151792: 1, 8,15, 57, 64,106,148, 400, 407, 449, 491, 743, 785,1037,1289
A151793: 1, 9,17, 73, 81,137,193, 585, 593, 649, 705,1097,1153,1545,1937
A255764: 1,10,19, 91,100,172,244, 820, 829, 901, 973,1549,1621,2197,2773
A255765: 1,11,21,111,121,211,301,1111,1121,1211,1301,2111,2201,3011,3821
A255766: 1,12,23,133,144,254,364,1464,1475,1585,1695,2795,2905,4005,5105
...

Index entries for sequences related to cellular automata

Rows 1-12: A000012, A070941, A005408, A151788, A147562, A151790, A151781, A151792, A151793, A255764, A255765, A255766.
Columns 1-10: A000012, A000027, A005408, A002061, A000290, A084849, A056107, A053698, A100705, A100104.
Cf. A000120, A255740.

A255744 a(1) = 1; for n > 1, a(n) = 10*9^(A000120(n-1)-1).

Original entry on oeis.org

1, 10, 10, 90, 10, 90, 90, 810, 10, 90, 90, 810, 90, 810, 810, 7290, 10, 90, 90, 810, 90, 810, 810, 7290, 90, 810, 810, 7290, 810, 7290, 7290, 65610, 10, 90, 90, 810, 90, 810, 810, 7290, 90, 810, 810, 7290, 810, 7290, 7290, 65610, 90, 810, 810, 7290, 810, 7290

Offset: 1

Omar E. Pol, Mar 05 2015

nonn

Also, this is a row of the square array A255740.

Partial sums give A255765.

			Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins:
1;
10;
10, 90;
10, 90, 90, 810;
10, 90, 90, 810, 90, 810, 810, 7290;
...

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Cf. A000120, A151787, A147582, A151789, A151779, A151791, A151782, A255740, A255741, A255743, A255745, A255765.

MapAt[Floor, Array[10*9^(DigitCount[# - 1, 2, 1] - 1) &, 54], 1] (* Michael De Vlieger, Nov 03 2022 *)

a(n) = if (n==1, 1, 10*9^(hammingweight(n-1)-1)); \\ Michel Marcus, Mar 15 2015

More terms from Michel Marcus, Mar 15 2015

A255764 Partial sums of A255743.

Original entry on oeis.org

1, 10, 19, 91, 100, 172, 244, 820, 829, 901, 973, 1549, 1621, 2197, 2773, 7381, 7390, 7462, 7534, 8110, 8182, 8758, 9334, 13942, 14014, 14590, 15166, 19774, 20350, 24958, 29566, 66430, 66439, 66511, 66583, 67159, 67231, 67807, 68383, 72991, 73063, 73639, 74215

Offset: 1

Omar E. Pol, Mar 05 2015

nonn

Also, this is a row of the square array A255741.

Michael De Vlieger, Table of n, a(n) for n = 1..16384
Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 33.

Cf. A005408, A151788, A147562, A151790, A151781, A151792, A151793, A255740, A255741, A255743, A255764, A255765, A255766.

Accumulate@ MapAt[Floor, Array[9*8^(DigitCount[# - 1, 2, 1] - 1) &, 43], 1] (* Michael De Vlieger, Nov 03 2022 *)

lista(nn) = {s = 1; for (n=2, nn, print1(s, ", "); s += 9*8^(hammingweight(n-1)-1););} \\ Michel Marcus, Mar 15 2015

More terms from Michel Marcus, Mar 15 2015

A255766 Partial sums of A255745.

Original entry on oeis.org

1, 12, 23, 133, 144, 254, 364, 1464, 1475, 1585, 1695, 2795, 2905, 4005, 5105, 16105, 16116, 16226, 16336, 17436, 17546, 18646, 19746, 30746, 30856, 31956, 33056, 44056, 45156, 56156, 67156, 177156, 177167, 177277, 177387, 178487, 178597, 179697, 180797, 191797

Offset: 1

Omar E. Pol, Mar 05 2015

nonn

Also, this is a row of the square array A255741.

Cf. A005408, A151788, A147562, A151790, A151781, A151792, A151793, A255740, A255741, A255745, A255764, A255765.

a(n) = sum(k=1, n, if (k==1, 1, 11*10^(hammingweight(k-1)-1)));

More terms from Michel Marcus, Mar 19 2015

cp's OEIS Frontend

A255741 Square array read by antidiagonals upwards: T(n,k), n>=1, k>=1, in which row n lists the partial sums of the n-th row of the square array of A255740.

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A255744 a(1) = 1; for n > 1, a(n) = 10*9^(A000120(n-1)-1).

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A255764 Partial sums of A255743.

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A255766 Partial sums of A255745.

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