|
| |
|
|
A055096
|
|
Triangle of sums of 2 distinct nonzero squares: (1^2+2^2), (1^2+3^2), (2^2+3^2), (1^2+4^2), (2^2+4^2), (3^2+4^2), ...
|
|
15
|
|
|
|
5, 10, 13, 17, 20, 25, 26, 29, 34, 41, 37, 40, 45, 52, 61, 50, 53, 58, 65, 74, 85, 65, 68, 73, 80, 89, 100, 113, 82, 85, 90, 97, 106, 117, 130, 145, 101, 104, 109, 116, 125, 136, 149, 164, 181, 122, 125, 130, 137, 146, 157, 170, 185, 202, 221, 145, 148, 153, 160
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Discovered by Bernard Frenicle de Bessy (1605?-1675). - Paul Curtz, Aug 18 2008
Terms that are not hypotenuses in primitive Pythagorean triangles, are replaced by 0 in A222946. - Reinhard Zumkeller, Mar 23 2013
|
|
|
LINKS
|
Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
A. Karttunen, Larger table, showing also locations of 4k+1 primes and squares
M. de Frenicle, Methode pour trouver la solutions des problems par les exclusions, in: Divers ouvrage des mathematique et de physique par messieurs de l'academie royale des science, (1693) pp 1-44.
Eric Weisstein's World of Mathematics, Congruum Problem.
Index entries for sequences related to sums of squares
|
|
|
FORMULA
|
a(n) = sum2distinct_squares_array(n).
T(n,k) = A133819(n,k) + A140978(n,k) = (n+1)^2 + k^2, 1 <= k < n. - Reinhard Zumkeller, Mar 23 2013
|
|
|
MAPLE
|
sum2distinct_squares_array := (n) -> (((n-((trinv(n-1)*(trinv(n-1)-1))/2))^2)+((trinv(n-1)+1)^2));
|
|
|
PROG
|
(Haskell)
a055096 n k = a055096_tabl !! (n-1) !! (k-1)
a055096_row n = a055096_tabl !! (n-1)
a055096_tabl = zipWith (zipWith (+)) a133819_tabl a140978_tabl
-- Reinhard Zumkeller, Mar 23 2013
|
|
|
CROSSREFS
|
Sorting gives A024507. Count of divisors: A055097, Moebius: A055132. For trinv, follow A055088. Left edge: A002522. Right edge: A001844. Central column: A033429.
Sequence in context: A004431 A025302 A221265 * A132777 A191217 A134961
Adjacent sequences: A055093 A055094 A055095 * A055097 A055098 A055099
|
|
|
KEYWORD
|
nonn,tabl,changed
|
|
|
AUTHOR
|
Antti Karttunen Apr 04 2000
|
|
|
STATUS
|
approved
|
| |
|
|
