Thursday, February 25, 2016

Sorry, I got carried away - the beginning of the 50th diagonal of Pascal's Triangle

Feb 25, 2016




The 50th Diagonal of Pascal’s Triangle:

A Sequence Number that generates the terms in the 50th diagonal of Pascal’s triangle, using 12 digit strings, is:
999,999,999,950,000,000,001,224,999,999,980,400,000,000,
230,299,999,997,881,240,000,015,890,699,999,900,115,600,
000,536,878,649,997,494,566,300,010,272,278,169,962,646,
261,200,121,399,651,099,645,139,481,400,937,845,656,297,
749,170,424,884,923,689,695,565,152,620,608,868,053,528,
883,744,594,056,616,847,129,212,243,892,672,553,937,288,
749,815,264,491,956,746,634,521,548,660,036,173,589,393,
562,369,548,660,036,191,956,746,634,488,749,815,264,532,
672,553,937,247,129,212,243,929,594,056,616,818,053,528,
883,765,152,620,608,854,923,689,695,572,749,170,424,880,
937,845,656,299,645,139,481,400,121,399,651,099,962,646,
261,200,010,272,278,169,997,494,566,300,000,536,878,649,
999,900,115,600,000,015,890,699,999,997,881,240,000,000,
230,299,999,999,980,400,000,000,001,224,999,999,999,950,
000,000,000,001.
The inverse of this number is:
1/999999999950000000001224999999980400000000230299
99999788124000001589069999990011560000053687864999
74945663000102722781699626462612001213996510996451
39481400937845656297749170424884923689695565152620
60886805352888374459405661684712921224389267255393
72887498152644919567466345215486600361735893935623
69548660036191956746634488749815264532672553937247
12921224392959405661681805352888376515262060885492
36896955727491704248809378456562996451394814001213
99651099962646261200010272278169997494566300000536
87864999990011560000001589069999999788124000000023
02999999999804000000000012249999999999500000000000
01 =
0.
000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000 000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000000  000000000001  000000000050  000000001275  000000022100  000000292825  000003162510  000028989675  000231917400  001652411475  010648873950  062828356305  ..
The first ten non-zero terms in this diagonal are accurately shown above.



David Brooks

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