|
%I #16 Sep 19 2013 10:02:18
%S 2,3,3,4,8,4,5,17,17,5,6,32,54,32,6,7,57,145,145,57,7,8,100,368,512,
%T 368,100,8,9,177,945,1649,1649,945,177,9,10,320,2530,5392,6250,5392,
%U 2530,320,10,11,593,7073,18785,23401,23401,18785,7073,593,11,12,1124,20412
%N A symmetrical powers triangle sequence: t(n,m) = (m^(n - m) + (n - m)^m).
%C Equivalently, table by antidiagonals of n^m + m^n for n,m > 0.
%C Row sums are:
%C {2, 6, 16, 44, 130, 418, 1464, 5560, 22754, 99726, 465536,...}.
%H Boris Putievskiy, <a href="/A156353/b156353.txt">Rows n = 1..77 of triangle, flattened</a>
%F t(n,m) = (m^(n - m) + (n - m)^m).
%F a(n) = A004736(n)^A002260(n) + A002260(n)^A004736(n) or
%F ((t*t+3*t+4)/2-n)^(n-(t*(t+1)/2))+ (n-(t*(t+1)/2))^((t*t+3*t+4)/2-n), where t=floor((-1+sqrt(8*n-7))/2). - _Boris Putievskiy_, Dec 14 2012
%e {2},
%e {3, 3},
%e {4, 8, 4},
%e {5, 17, 17, 5},
%e {6, 32, 54, 32, 6},
%e {7, 57, 145, 145, 57, 7},
%e {8, 100, 368, 512, 368, 100, 8},
%e {9, 177, 945, 1649, 1649, 945, 177, 9},
%e {10, 320, 2530, 5392, 6250, 5392, 2530, 320, 10},
%e {11, 593, 7073, 18785, 23401, 23401, 18785, 7073, 593, 11},
%e {12, 1124, 20412, 69632, 94932, 93312, 94932, 69632, 20412, 1124, 12}
%t Clear[t, n, m];
%t t[n_, m_] = (m^(n - m) + (n - m)^m);
%t Table[Table[t[n, m], {m, 1, n - 1}], {n, 2, 12}];
%t Flatten[%]
%o (Python)
%o t=int((math.sqrt(8*n-7) - 1)/ 2)
%o m=((t*t+3*t+4)/2-n)**(n-t*(t+1)/2)+(n-t*(t+1)/2)**((t*t+3*t+4)/2-n)
%o # _Boris Putievskiy_, Dec 14 2012
%Y Cf. A005652 is the same table with row 0 and column 0 included.
%K nonn,tabl
%O 1,1
%A _Roger L. Bagula_, Feb 08 2009
%E Edited by _Franklin T. Adams-Watters_, Oct 26 2009
|
