Square triangular number: Difference between revisions

Revision as of 22:43, 9 November 2022

Revision as of 05:27, 10 November 2022

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==Numerical data==

As {{mvar|k}} becomes larger, the ratio {{math|{{sfrac|''t_k''|''s_k''}}}} approaches [[square root of 2|{{sqrt|2}}]] ≈ {{val|1.41421356}}, and the ratio of successive square triangular numbers approaches {{nowrap|(1 + {{sqrt|2}})⁴}} {{nowrap|{{=}} 17 + 12{{sqrt|2}}}} ≈ {{val|33.970562748}}. The table below shows values of {{mvar|k}} between 0 and 1411, which comprehend all square triangular numbers up to {{val||e=2116}}.

:{| class="wikitable" border="1" style="text-align:right"

Line 204:

|align=left|{{val|1.41421355}}

|align=left|{{val|33.970562748}}

The|}<!-- rows of theThe table for k up to 11 (inclusive) werewas generated onin 23-jul-2016 using a Python script available at http://pastebin.com/sWyesrR8 -->

|-

|12

|73 804 512 832 419 600

|271 669 860

|384 199 200

|1.414 213 560 532 626

|33.970 562 748 477

|-

|13

|2 507 180 834 294 496 361

|1 583 407 981

|2 239 277 041

|1.414 213 562 057 320

|33.970 562 748 477

|-

|14

|85 170 343 853 180 456 676

|9 228 778 026

|13 051 463 048

|1.414 213 562 318 917

|33.970 562 748 477

|}<!-- The table was generated programmatically.

The rows of the table for k up to 11 (inclusive) were generated on 23-jul-2016 using a Python script available at http://pastebin.com/sWyesrR8

The values for following rows were generated on 09-nov-2022 using a Rust program available at https://pastebin.com/2MzYiJdP -->

==See also==