The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A208855 Array of even catheti of primitive Pythagorean triangles when read by SW-NE diagonals. 4
 4, 12, 8, 20, 24, 12, 28, 40, 0, 16, 36, 56, 60, 48, 20, 44, 72, 84, 80, 60, 24, 52, 88, 0, 112, 0, 0, 28, 60, 104, 132, 144, 140, 120, 84, 32, 68, 120, 156, 176, 180, 168, 140, 96, 36, 76, 136, 0, 208, 220, 0, 0, 160, 0, 40 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See the comments, reference and links in A208853. The present array is b(n,m) = 2*(2*n-1)*(2*m)  if gcd((2*n-1,2*m)=1 and 0 otherwise.  u=2*n-1, v=2*m. The array read by SW-NE diagonals is T(n,m):=b(n-m+1,m), n>=m>=1. All primitive Pythagorean triples are given by (a(n,m)=A208854(n,m),b(n,m),c(n,m)= A208853(n,m)), n>=1, m>=1. If the entry is 0 there is no primitive Pythagorean triple for these n and m values. LINKS FORMULA T(n,m)=b(n-m+1,m), n>=m>=1, with b(n,m):= 4*(2*n-1)*m if gcd((2*n-1,2*m)=1 and 0 otherwise. EXAMPLE Array b(n,m): ........m|  1    2     3     4    5    6    7    8    9    10 ... ........v|  2    4     6     8   10   12   14   16   18    20 n,  u 1,  1       4    8    12    16   20   24   28   32   36    40 2,  3      12   24     0    48   60    0   84   96    0   120 3,  5      20   40    60    80    0  120  140  160  180     0 4,  7      28   56    84   112  140  168    0  224  252   280 5,  9      36   72     0   144  180    0  252  288    0   360 6, 11      44   88   132   176  220  264  308  352  396   440 7, 13      52  104   156   208  260  312  364  416  468   520 8, 15      60  120     0   240    0    0  420  480    0     0 9, 17      68  136   204   272  340  408  476  544  612   680 10,19      76  152   228   304  380  456  532  608  684   760 ... Triangle T(n,m): ......m|  1     2     3      4     5     6     7     8    9  10 ......v|  2     4     6      8    10   12     14    16   18  20 n,  u 1,  1     4 2,  3    12     8 3,  5    20    24    12 4,  7    28    40     0     16 5,  9    36    56    60     48    20 6, 11    44    72    84     80    60   24 7, 13    52    88     0    112     0    0     28 8, 15    60   104   132    144   140  120     84    32 9, 17    68   120   156    176   180  168    140    96   36 10,19    76   136     0    208   220    0      0   160    0  40 ... For some triples see the example section of A208853. CROSSREFS Cf. A208853, A208854. Sequence in context: A310569 A145046 A205849 * A252984 A084415 A156681 Adjacent sequences:  A208852 A208853 A208854 * A208856 A208857 A208858 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang, Mar 05 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 18 10:07 EDT 2021. Contains 343087 sequences. (Running on oeis4.)