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.

Previous Showing 31-36 of 36 results.

A169941 Triangle read by rows: A169940 with rows reversed.

Original entry on oeis.org

1, 1, 1, 1, 0, 3, 1, 1, 3, 3, 1, 0, 6, 4, 5, 1, 1, 6, 10, 7, 7, 1, 0, 9, 6, 27, 8, 13, 1, 1, 9, 17, 23, 41, 21, 15, 1, 0, 12, 8, 56, 34, 98, 20, 27, 1, 1, 12, 22, 50, 104, 96, 148, 53, 25, 1, 0, 15, 10, 96, 66, 294, 116, 325, 56, 45, 1, 1, 15, 27, 86, 184, 262, 518, 319
Offset: 1

Views

Author

N. J. A. Sloane, Aug 01 2010

Keywords

Examples

			Triangle begins:
[1]
[1, 1]
[1, 0, 3]
[1, 1, 3, 3]
[1, 0, 6, 4, 5]
[1, 1, 6, 10, 7, 7]
[1, 0, 9, 6, 27, 8, 13]
[1, 1, 9, 17, 23, 41, 21, 15]
[1, 0, 12, 8, 56, 34, 98, 20, 27]
[1, 1, 12, 22, 50, 104, 96, 148, 53, 25]
[1, 0, 15, 10, 96, 66, 294, 116, 325, 56, 45]
[1, 1, 15, 27, 86, 184, 262, 518, 319, 487, 89, 59]
[1, 0, 18, 12, 143, 112, 608, 346, 1279, 434, 942, 112, 89]
[1, 1, 18, 32, 131, 291, 528, 1166, 1153, 2181, 1042, 1348, 197, 103]
[1, 0, 21, 14, 199, 168, 1083, 720, 3313, 1568, 4981, 1320, 2613, 220, 163]
...

Links

Crossrefs

Related to thickness: A169940-A169954, A061909.

Formula

Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?

A169943 Second entry in row n of triangle in A169940.

Original entry on oeis.org

1, 0, 3, 4, 7, 8, 21, 20, 53, 56, 89, 112, 197, 220, 397, 456, 711, 850, 1347, 1428, 2303, 2642, 3777, 4636, 6693, 7550, 11109, 12876, 17965, 21000, 29207, 32952, 46263, 53372, 71069, 82660, 111877, 126042, 172461, 195898, 256577
Offset: 2

Views

Author

N. J. A. Sloane, Aug 01 2010

Keywords

Comments

Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?

Links

Crossrefs

Related to thickness: A169940-A169954, A061909.

Programs

  • Mathematica
    (* Very slow *) a[n_] := Module[{dd, xx, mm}, dd = Join[{1}, PadLeft[ IntegerDigits[#, 2], n - 1], {1}] & /@ Range[0, 2^(n - 1) - 1]; xx = (((x^Range[n, 0, -1]).#) & /@ dd)^2 // Expand; mm = Max[ CoefficientList[ #, x]] & /@ xx; Count[mm, 3]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 2, 20}] (* Jean-François Alcover, Oct 10 2017 *)

Formula

a(n) = A169953(n) - A169953(n-1) for n>2.

Extensions

a(15)-a(30) from Nathaniel Johnston, Nov 12 2010
a(31)-a(42) from Andrew Howroyd, Jul 09 2017

A169944 Maximal entry in row n of triangle in A169940.

Original entry on oeis.org

1, 1, 3, 3, 6, 10, 27, 41, 98, 148, 325, 518, 1279, 2181, 4981, 8393, 17730, 28938, 67290, 120550, 267894, 469928, 998433, 1725367, 3719207, 6830683, 15021379, 27155069, 57664535, 102865259
Offset: 1

Views

Author

N. J. A. Sloane, Aug 01 2010

Keywords

Links

Crossrefs

Related to thickness: A169940-A169954, A061909.

Formula

Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?

Extensions

a(16)-a(30) from Nathaniel Johnston, Nov 12 2010

A169946 Triangle read by rows: A169945 with rows reversed.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 8, 4, 1, 1, 3, 6, 16, 5, 1, 1, 2, 11, 14, 29, 6, 1, 1, 3, 9, 29, 29, 49, 7, 1, 1, 2, 14, 22, 74, 52, 82, 8, 1, 1, 3, 12, 42, 58, 160, 96, 130, 9, 1, 1, 2, 17, 30, 126, 128, 344, 160, 205, 10, 1, 1, 3, 15, 53, 98, 314, 294, 676, 277, 305, 11
Offset: 0

Views

Author

N. J. A. Sloane, Aug 01 2010

Keywords

Comments

The heuristic formula for the third column (verified for 2<=n<=21) is 3*n/2+7*(1-(-1)^n)/4. [From R. J. Mathar, Aug 02 2010]

Examples

			Triangle begins:
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 2, 8, 4, 1]
[1, 3, 6, 16, 5, 1]
[1, 2, 11, 14, 29, 6, 1]
[1, 3, 9, 29, 29, 49, 7, 1]
[1, 2, 14, 22, 74, 52, 82, 8, 1]
[1, 3, 12, 42, 58, 160, 96, 130, 9, 1]
[1, 2, 17, 30, 126, 128, 344, 160, 205, 10, 1]
[1, 3, 15, 53, 98, 314, 294, 676, 277, 305, 11, 1]
[1, 2, 20, 38, 185, 232, 796, 576, 1333, 450, 450, 12, 1]
[1, 3, 18, 64, 147, 501, 628, 1796, 1177, 2477, 712, 654, 13, 1]
[1, 2, 23, 46, 251, 368, 1425, 1370, 4075, 2212, 4563, 1086, 947, 14, 1]
[1, 3, 21, 75, 205, 729, 1117, 3515, 3265, 8535, 4289, 7997, 1657, 1343, 15, 1]
...

Links

Crossrefs

Related to thickness: A169940-A169954, A061909.

Formula

Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?

A169949 Maximal entry in row n of triangle in A169945.

Original entry on oeis.org

1, 2, 3, 8, 16, 29, 49, 82, 160, 344, 676, 1333, 2477, 4563, 8535, 17976, 35810, 71374, 135876, 258898, 476494, 981244, 1962600, 3942389, 7647545, 14879679, 28109033, 55334514, 111234624
Offset: 0

Views

Author

N. J. A. Sloane, Aug 01 2010

Keywords

Links

Crossrefs

Related to thickness: A169940-A169954, A061909.

Formula

Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?

Extensions

a(15)-a(28) from Nathaniel Johnston, Nov 12 2010

A169951 Triangle read by rows: A169950 with rows reversed.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 2, 4, 8, 1, 1, 1, 8, 8, 13, 1, 1, 2, 7, 18, 15, 20, 1, 1, 1, 11, 13, 45, 23, 33, 1, 1, 2, 10, 28, 36, 86, 44, 48, 1, 1, 1, 14, 18, 84, 70, 184, 64, 75, 1, 1, 2, 13, 36, 68, 188, 166, 332, 117, 100, 1, 1, 1, 17, 23, 132, 134, 482, 282, 657
Offset: 0

Views

Author

N. J. A. Sloane, Aug 01 2010

Keywords

Examples

			Triangle begins:
[1]
[1, 1]
[1, 2, 1]
[1, 1, 5, 1]
[1, 2, 4, 8, 1]
[1, 1, 8, 8, 13, 1]
[1, 2, 7, 18, 15, 20, 1]
[1, 1, 11, 13, 45, 23, 33, 1]
[1, 2, 10, 28, 36, 86, 44, 48, 1]
[1, 1, 14, 18, 84, 70, 184, 64, 75, 1]
[1, 2, 13, 36, 68, 188, 166, 332, 117, 100, 1]
[1, 1, 17, 23, 132, 134, 482, 282, 657, 173, 145, 1]
[1, 2, 16, 44, 109, 316, 396, 1000, 601, 1144, 262, 204, 1]
[1, 1, 20, 28, 187, 221, 924, 742, 2279, 1035, 2086, 374, 293, 1]
[1, 2, 19, 52, 159, 478, 749, 2090, 1895, 4460, 2077, 3434, 571, 396, 1]
[1, 1, 23, 33, 251, 327, 1561, 1469, 5403, 3463, 9441, 3397, 6047, 791, 559, 1]
...

Links

Crossrefs

Related to thickness: A169940-A169954, A061909.

Formula

Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?
Previous Showing 31-36 of 36 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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