cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A255557 Square array A(row,col): A(1,1) = 1, A(1,col) = A055938(col-1), and for row > 1: A(row,col) = A005187(1+A(row-1,col)).

Original entry on oeis.org

1, 2, 3, 5, 4, 7, 6, 10, 8, 15, 9, 11, 19, 16, 31, 12, 18, 22, 38, 32, 63, 13, 23, 35, 42, 74, 64, 127, 14, 25, 46, 70, 82, 146, 128, 255, 17, 26, 49, 89, 138, 162, 290, 256, 511, 20, 34, 50, 97, 176, 274, 322, 578, 512, 1023, 21, 39, 67, 98, 193, 350, 546, 642, 1154, 1024, 2047, 24, 41, 78, 134, 194, 385, 695, 1090, 1282, 2306, 2048, 4095
Offset: 1

Views

Author

Antti Karttunen, Apr 13 2015

Keywords

Comments

The array is read by antidiagonals: A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
This is transpose of array A255555, see comments and links given there.

Examples

			The top left corner of the array:
     1,    2,    5,    6,    9,   12,   13,   14,   17,   20,    21,    24
     3,    4,   10,   11,   18,   23,   25,   26,   34,   39,    41,    47
     7,    8,   19,   22,   35,   46,   49,   50,   67,   78,    81,    94
    15,   16,   38,   42,   70,   89,   97,   98,  134,  153,   161,   184
    31,   32,   74,   82,  138,  176,  193,  194,  266,  304,   321,   365
    63,   64,  146,  162,  274,  350,  385,  386,  530,  606,   641,   726
   127,  128,  290,  322,  546,  695,  769,  770, 1058, 1207,  1281,  1447
   255,  256,  578,  642, 1090, 1387, 1537, 1538, 2114, 2411,  2561,  2891
   511,  512, 1154, 1282, 2178, 2770, 3073, 3074, 4226, 4818,  5121,  5778
  1023, 1024, 2306, 2562, 4354, 5535, 6145, 6146, 8450, 9631, 10241, 11551
  ...

Links

Crossrefs

Inverse permutation: A255558.
Transpose: A255555.
Column 1: A000225.
Cf. A005187, A055938.
Cf. A255559 (row index), A255560 (column index).
Cf. also A254107, A256997 (variants).

Programs

Formula

A(row,col): A(1,1) = 1, and for the rest of topmost row: A(1,col) = A055938(col-1), and for any row > 1: A(row,col) = A005187(1+A(row-1,col)).

A255556 Inverse permutation to A255555.

Original entry on oeis.org

1, 3, 2, 5, 6, 10, 4, 8, 15, 9, 14, 21, 28, 36, 7, 12, 45, 20, 13, 55, 66, 19, 27, 78, 35, 44, 91, 105, 120, 136, 11, 17, 153, 54, 26, 171, 190, 18, 65, 210, 77, 25, 231, 253, 276, 34, 90, 300, 43, 53, 325, 351, 104, 119, 378, 135, 152, 406, 435, 465, 496, 528, 16, 23, 561, 170, 64, 595, 630, 33, 189, 666, 209, 24
Offset: 1

Views

Author

Antti Karttunen, Apr 14 2015

Keywords

Links

Crossrefs

Inverse permutation: A255555.
Cf. A255558, A255559, A255560.

Programs

  • Scheme
    (define (A255556 n) (let ((col (A255559 n)) (row (A255560 n))) (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))

Formula

a(n) = (1/2) * ((c+r)^2 - r - 3*c + 2), where c = A255559(n), and r = A255560(n).

A256998 Inverse to A256997 considered as a permutation of natural numbers, with the assumed fixed term a(1) = 1.

Original entry on oeis.org

1, 2, 4, 7, 3, 5, 11, 6, 8, 9, 16, 12, 17, 23, 10, 13, 30, 14, 22, 38, 47, 18, 24, 57, 31, 15, 68, 80, 93, 107, 19, 39, 122, 20, 29, 138, 155, 48, 58, 173, 25, 32, 192, 212, 233, 69, 40, 255, 21, 81, 278, 302, 94, 108, 327, 123, 26, 353, 380, 408, 437, 467, 49, 139, 498, 27, 37, 530, 563, 156, 174, 597, 59, 70, 632, 668, 705, 193, 33, 743, 41
Offset: 1

Views

Author

Antti Karttunen, Apr 14 2015

Keywords

Links

Crossrefs

Inverse: A256997.
Cf. A256989, A256990.
Cf. also A256996, A255558.

Programs

  • Scheme
    (define (A256998 n) (if (= 1 n) n (let ((row (A256989 n)) (col (A256990 n))) (+ 1 (* (/ 1 2) (- (expt (+ row col) 2) row col col col -2))))))

Formula

a(1) = 1, and for n > 1: a(n) = (1/2) * ((c+r)^2 - r - 3*c + 4), where r = A256989(n), and c = A256990(n).
Showing 1-3 of 3 results.

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