A297191 -id:A297191 - cp's OEIS frontend

A297192 Left-hand half of triangle A297191.

1, 1, 3, 1, 7, 13, 1, 11, 41, 63, 1, 15, 85, 231, 321, 1, 19, 145, 575, 1289, 1683, 1, 23, 221, 1159, 3649, 7183, 8989, 1, 27, 313, 2047, 8361, 22363, 40081, 48639, 1, 31, 421, 3303, 16641, 56695, 134245, 224143, 265729, 1, 35, 545, 4991, 29961, 124515, 369305

Offset: 0

N. J. A. Sloane, Jan 10 2018

Rémy Sigrist, Rows n = 0..100 of triangle, flattened
Rémy Sigrist, PARI program for A297192

Cf. A008288, A297191.

PARI
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See Links section.
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More terms from Rémy Sigrist, Jan 19 2018

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

Original entry on oeis.org

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

A297192 Left-hand half of triangle A297191.

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