A188474 -id:A188474 - cp's OEIS frontend

A188476 Diagonal sums of number triangle A188474.

1, 1, 2, 6, 12, 27, 65, 150, 353, 843, 2014, 4843, 11713, 28433, 69292, 169470, 415754, 1022868, 2523120, 6238645, 15459561, 38387191, 95497612, 237989801, 594062697, 1485141397, 3718116380, 9320941698, 23396109986, 58795356627, 147920737819

Offset: 0

Paul Barry, Apr 01 2011

Hankel transform is A188477(n+1).

a(n)=sum{k=0..floor(n/2), sum{j=0..n-2k+1, (j/(n-k+2-j))*C(n-k+2-j,n-k+1)*C(n-k+2-j,k+1)*2^(j-1)}}.

Conjecture: (n+3)*a(n) +(-4*n-9)*a(n-1) +n*a(n-2) -3*a(n-3) +3*(5*n+1)*a(n-4) +6*(n)*a(n-5) +6*(n-1)*a(n-6) +4*(-n+3)*a(n-7)=0. - R. J. Mathar, Dec 03 2014

A188461 A Deutsch-Fibonacci triangle.

Original entry on oeis.org

1, 1, 1, 1, 5, 1, 1, 10, 10, 1, 1, 16, 39, 16, 1, 1, 23, 99, 99, 23, 1, 1, 31, 203, 375, 203, 31, 1, 1, 40, 366, 1065, 1065, 366, 40, 1, 1, 50, 605, 2521, 4027, 2521, 605, 50, 1, 1, 61, 939, 5266, 12220, 12220, 5266, 939, 61, 1

Offset: 0

Paul Barry, Apr 01 2011

Second column is A052905. Third column is A188480.

			Triangle begins
1,
1, 1,
1, 5, 1,
1, 10, 10, 1,
1, 16, 39, 16, 1,
1, 23, 99, 99, 23, 1,
1, 31, 203, 375, 203, 31, 1,
1, 40, 366, 1065, 1065, 366, 40, 1,
1, 50, 605, 2521, 4027, 2521, 605, 50, 1,
1, 61, 939, 5266, 12220, 12220, 5266, 939, 61, 1

Cf. A100754, A188474.

T(n,k)=sum{j=0..n-k+1, (j/(n+2-j))C(n+2-j,n-k+1)*C(n+2-j,k+1)*F(j+1)}.

cp's OEIS Frontend

A188476 Diagonal sums of number triangle A188474.

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