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

0,3

Links

Table of n, a(n) for n=0..59.

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.

Example

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,
...

Maple

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

Crossrefs

Cf. A008288, A297191, A297194.

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

Sequence in context: A316932 A317703 A055107 * A272867 A206438 A331148

Adjacent sequences: A297190 A297191 A297192 * A297194 A297195 A297196

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 10 2018

Status

approved