A100754 -id:A100754 - cp's OEIS frontend

A188444 Expansion of (1+x)(1+x+x^2)(1-x+x^2-4*x+x^4-x^5+x^6)/(1+x^4)^3.

1, 1, 1, -3, -9, -9, -6, 10, 25, 25, 15, -21, -49, -49, -28, 36, 81, 81, 45, -55, -121, -121, -66, 78, 169, 169, 91, -105, -225, -225, -120, 136, 289, 289, 153, -171, -361, -361, -190, 210, 441, 441, 231, -253, -529, -529, -276, 300, 625, 625, 325

Offset: 0

Paul Barry, Mar 31 2011

a(n+1) is the Hankel transform of A166300(n+3) (diagonal sums of the triangle A100754).

Index entries for linear recurrences with constant coefficients, signature (0,0,0,-3,0,0,0,-3,0,0,0,-1).

G.f.: (1+x+x^2-3*x^3-6*x^4-6*x^5-3*x^6+x^7+x^8+x^9)/(1+x^4)^3.

a(n) = -3*a(n-4) - 3*a(n-8) - a(n-12). - Wesley Ivan Hurt, Mar 17 2023

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

A188444 Expansion of (1+x)(1+x+x^2)(1-x+x^2-4*x+x^4-x^5+x^6)/(1+x^4)^3.

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A188461 A Deutsch-Fibonacci triangle.

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cp's OEIS Frontend

A188444 Expansion of (1+x)*(1+x+x^2)*(1-x+x^2-4*x+x^4-x^5+x^6)/(1+x^4)^3.

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Author

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Formula

A188461 A Deutsch-Fibonacci triangle.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A188444 Expansion of (1+x)(1+x+x^2)(1-x+x^2-4*x+x^4-x^5+x^6)/(1+x^4)^3.