A117352 -id:A117352 - cp's OEIS frontend

A117353 Expansion of (1-x)/(1-3x+x^2+4x^3-4x^4).

1, 2, 5, 9, 18, 33, 65, 126, 253, 505, 1018, 2041, 4097, 8198, 16405, 32793, 65570, 131089, 262145, 524238, 1048493, 2097017, 4194186, 8388521, 16777281, 33554646, 67109317, 134218265, 268436018, 536871105, 1073741505, 2147482398

Offset: 0

Paul Barry, Mar 09 2006

Diagonal sums of number triangle A117352.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-4,4).

G.f.: (1-x)/((1-2x)(1-x-x^2+2x^3)); a(n)=3a(n-1)-a(n-2)-4a(n-3)+4a(n-4); a(n)=sum{k=0..floor(n/2), sum{j=0..n-2k, C(j-k,j)C(n-2k,j)}}.

A117354 Riordan array ((1-x+sqrt(1-6x+x^2))/2, (1+x-sqrt(1-6x+x^2))/4).

Original entry on oeis.org

1, -2, 1, -2, -1, 1, -6, -1, 0, 1, -22, -3, 1, 1, 1, -90, -11, 4, 4, 2, 1, -394, -45, 17, 16, 8, 3, 1, -1806, -197, 76, 69, 34, 13, 4, 1, -8558, -903, 353, 313, 153, 59, 19, 5, 1, -41586, -4279, 1688, 1472, 716, 278, 92, 26, 6, 1, -206098, -20793, 8257, 7112, 3448, 1346, 454, 134, 34

Offset: 0

Paul Barry, Mar 09 2006

First column is A085403. Row sums are A086456. Inverse of A117352.

			Triangle begins
1,
-2, 1,
-2, -1, 1,
-6, -1, 0, 1,
-22, -3, 1, 1, 1,
-90, -11, 4, 4, 2, 1,
-394, -45, 17, 16, 8, 3, 1

cp's OEIS Frontend

A117353 Expansion of (1-x)/(1-3x+x^2+4x^3-4x^4).

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A117354 Riordan array ((1-x+sqrt(1-6x+x^2))/2, (1+x-sqrt(1-6x+x^2))/4).

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