A156353 A symmetrical powers triangle sequence: t(n,m) = (m^(n - m) + (n - m)^m).

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, 368, 100, 8, 9, 177, 945, 1649, 1649, 945, 177, 9, 10, 320, 2530, 5392, 6250, 5392, 2530, 320, 10, 11, 593, 7073, 18785, 23401, 23401, 18785, 7073, 593, 11, 12, 1124, 20412

Offset: 1

Author

Roger L. Bagula, Feb 08 2009

Keywords

• nonn
• tabl

Comments

Equivalently, table by antidiagonals of n^m + m^n for n,m > 0.

Row sums are:

{2, 6, 16, 44, 130, 418, 1464, 5560, 22754, 99726, 465536,...}.

Examples

			{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, 368, 100, 8},
{9, 177, 945, 1649, 1649, 945, 177, 9},
{10, 320, 2530, 5392, 6250, 5392, 2530, 320, 10},
{11, 593, 7073, 18785, 23401, 23401, 18785, 7073, 593, 11},
{12, 1124, 20412, 69632, 94932, 93312, 94932, 69632, 20412, 1124, 12}
		

Links

• Boris Putievskiy, Rows n = 1..77 of triangle, flattened

Crossrefs

Cf. A005652 is the same table with row 0 and column 0 included.

Programs

Mathematica

Clear[t, n, m];
t[n_, m_] = (m^(n - m) + (n - m)^m);
Table[Table[t[n, m], {m, 1, n - 1}], {n, 2, 12}];
Flatten[%]

Python

t=int((math.sqrt(8*n-7) - 1)/ 2)
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)
# Boris Putievskiy, Dec 14 2012

Formula

t(n,m) = (m^(n - m) + (n - m)^m).

a(n) = A004736(n)^A002260(n) + A002260(n)^A004736(n) or

((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

Extensions

Edited by Franklin T. Adams-Watters, Oct 26 2009