A089383 -id:A089383 - cp's OEIS frontend

A297193 Irregular triangle read by rows: rows are partial alternating sums of rows of A297191.

1, 1, 4, 1, 1, 8, 17, 8, 1, 1, 12, 49, 80, 49, 12, 1, 1, 16, 97, 280, 401, 280, 97, 16, 1, 1, 20, 161, 672, 1569, 2084, 1569, 672, 161, 20, 1, 1, 24, 241, 1320, 4321, 8752, 11073, 8752, 4321, 1320, 241, 24, 1, 1, 28, 337, 2288, 9681, 26684, 48833, 59712, 48833, 26684, 9681

Offset: 0

N. J. A. Sloane, Jan 10 2018

			Triangle begins:
1,
1,4,1,
1,8,17,8,1,
1,12,49,80,49,12,1,
1,16,97,280,401,280,97,16,1,
1,20,161,672,1569,2084,1569,672,161,20,1,
...

I. Sugai, Numerical solutions of Laplace's Equation, given Cauchy conditions, IBM Journal 3 (1959), 187-188. (Annotated scanned copy.) A signed version of the triangle appears on page 188, but the signs are not important.

Cf. A008288, A297191, A297194.

The middle and next to middle columns are A089165 and A089383.

A297191x := proc(n,k)
    A008288(2*n+1,k) ;
end proc:
A297193 := proc(n,k)
    add((-1)^(i+1)*A297191x(n,i),i=0..k) ;
    abs(%) ;
end proc:
seq(seq(A297193(n,k),k=0..2*n),n=0..10) ; # R. J. Mathar, Mar 04 2018

cp's OEIS Frontend

A297193 Irregular triangle read by rows: rows are partial alternating sums of rows of A297191.

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