A161447 -id:A161447 - cp's OEIS frontend

A161450 Numbers n such that A160700(n) = 10.

10, 27, 40, 57, 78, 95, 108, 125, 130, 147, 160, 177, 198, 215, 228, 245, 267, 282, 297, 312, 335, 350, 365, 380, 387, 402, 417, 432, 455, 470, 485, 500, 520, 537, 554, 571, 588, 605, 622, 639, 640, 657, 674, 691, 708, 725, 742, 759, 777, 792, 811, 826, 845

Offset: 1

Reinhard Zumkeller, Jun 10 2009

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161451, A161452, A161453, A161454, A161455.

A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==10, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161451 Numbers n such that A160700(n) = 11.

Original entry on oeis.org

11, 26, 41, 56, 79, 94, 109, 124, 131, 146, 161, 176, 199, 214, 229, 244, 266, 283, 296, 313, 334, 351, 364, 381, 386, 403, 416, 433, 454, 471, 484, 501, 521, 536, 555, 570, 589, 604, 623, 638, 641, 656, 675, 690, 709, 724, 743, 758, 776, 793, 810, 827, 844

Offset: 1

Reinhard Zumkeller, Jun 10 2009

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161452, A161453, A161454, A161455.

A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==11, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161452 Numbers m such that A160700(m) = 12.

Original entry on oeis.org

12, 29, 46, 63, 72, 89, 106, 123, 132, 149, 166, 183, 192, 209, 226, 243, 269, 284, 303, 318, 329, 344, 363, 378, 389, 404, 423, 438, 449, 464, 483, 498, 526, 543, 556, 573, 586, 603, 616, 633, 646, 663, 676, 693, 706, 723, 736, 753, 783, 798, 813, 828, 843

Offset: 1

Reinhard Zumkeller, Jun 10 2009

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161453, A161454, A161455.

A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==12, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161453 Numbers n such that A160700(n) = 13.

Original entry on oeis.org

13, 28, 47, 62, 73, 88, 107, 122, 133, 148, 167, 182, 193, 208, 227, 242, 268, 285, 302, 319, 328, 345, 362, 379, 388, 405, 422, 439, 448, 465, 482, 499, 527, 542, 557, 572, 587, 602, 617, 632, 647, 662, 677, 692, 707, 722, 737, 752, 782, 799, 812, 829, 842

Offset: 1

Reinhard Zumkeller, Jun 10 2009

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161454, A161455.

A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==13, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161454 Numbers n such that A160700(n) = 14.

Original entry on oeis.org

14, 31, 44, 61, 74, 91, 104, 121, 134, 151, 164, 181, 194, 211, 224, 241, 271, 286, 301, 316, 331, 346, 361, 376, 391, 406, 421, 436, 451, 466, 481, 496, 524, 541, 558, 575, 584, 601, 618, 635, 644, 661, 678, 695, 704, 721, 738, 755, 781, 796, 815, 830, 841

Offset: 1

Reinhard Zumkeller, Jun 10 2009

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161455.

A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==14, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A161455 Numbers n such that A160700(n) = 15.

Original entry on oeis.org

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 270, 287, 300, 317, 330, 347, 360, 377, 390, 407, 420, 437, 450, 467, 480, 497, 525, 540, 559, 574, 585, 600, 619, 634, 645, 660, 679, 694, 705, 720, 739, 754, 780, 797, 814, 831, 840

Offset: 1

Reinhard Zumkeller, Jun 10 2009

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A161440, A161441, A161442, A161443, A161444, A161445, A161446, A161447, A161448, A161449, A161450, A161451, A161452, A161453, A161454.

A160700(n)=my(t=n%16); while(n>15, n>>=4; t=bitxor(t, n%16)); t
a(n)=for(k=16*n-16, 16*n-1, if(a(k)==15, return(k))) \\ Charles R Greathouse IV, Jan 25 2018

16n - 16 <= a(n) <= 16n - 1. - Charles R Greathouse IV, Jan 25 2018

A360962 Square array T(n,k) = k((3+6n)*k - 1)/2; n>=0, k>=0, read by antidiagonals upwards.

Original entry on oeis.org

0, 0, 1, 0, 4, 5, 0, 7, 17, 12, 0, 10, 29, 39, 22, 0, 13, 41, 66, 70, 35, 0, 16, 53, 93, 118, 110, 51, 0, 19, 65, 120, 166, 185, 159, 70, 0, 22, 77, 147, 214, 260, 267, 217, 92, 0, 25, 89, 174, 262, 335, 375, 364, 284, 117, 0, 28, 101, 201, 310, 410, 483, 511, 476, 360, 145

Offset: 0

Paul Curtz, Feb 27 2023

The main diagonal is A024394.

The antidiagonals sums are A000537.

			The rows are:
  0  1  5  12  22  35  51  70 ... = A000326
  0  4 17  39  70 110 159 217 ... = A022266
  0  7 29  66 118 185 267 364 ... = A022272
  0 10 41  93 166 260 375 511 ... = A022278
  0 13 53 120 214 335 483 658 ... = A022284
  ... .
Columns: A000004, A016777, A017581, A154266=3*A017209, 2*A348845, 5*A161447, 3*A158057(n+1), ... (coefficients from A026741).
Difference between two consecutive rows are: A033428.
This square array read by antidiagonals leads to the triangle
  0
  0  1
  0  4  5
  0  7 17 12
  0 10 29 39  22
  0 13 41 66  70  35
  0 16 53 93 118 110 51
  ... .

Cf. A000326, A000537, A022266, A022272, A022278, A022284, A024394.
Cf. A033428.
Cf. A000004, A016777, A017209, A017581, A026741, A154266, A158057, A161447, A348845.

T:= (n,k)-> k*(k*(3+6*n)-1)/2:
seq(seq(T(d-k,k), k=0..d), d=0..10);  # Alois P. Heinz, Feb 28 2023

T[n_, k_] := ((6*n + 3)*k - 1)*k/2; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Feb 27 2023 *)

T(n,k) = k*((3+6*n)*k-1)/2; \\ Michel Marcus, Feb 27 2023

Take successively sequences n*(3*n-1)/2, n*(9*n-1)/2, n*(15*n-1)/2, n*(21*n-1)/2, ... listed in the EXAMPLE section.
From Stefano Spezia, Feb 21 2024: (Start)
G.f.: y*(1 + 2*y + x*(2 + y))/((1 - x)^2*(1 - y)^3).
E.g.f.: exp(x+y)*y*(2 + 3*y + 6*x*(1 + y))/2. (End)

cp's OEIS Frontend

A161450 Numbers n such that A160700(n) = 10.

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A161451 Numbers n such that A160700(n) = 11.

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A161452 Numbers m such that A160700(m) = 12.

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A161453 Numbers n such that A160700(n) = 13.

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A161454 Numbers n such that A160700(n) = 14.

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A161455 Numbers n such that A160700(n) = 15.

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A360962 Square array T(n,k) = k*((3+6*n)*k - 1)/2; n>=0, k>=0, read by antidiagonals upwards.

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A360962 Square array T(n,k) = k((3+6n)*k - 1)/2; n>=0, k>=0, read by antidiagonals upwards.