A099605 -id:A099605 - cp's OEIS frontend

A099606 Row sums of triangle A099605, in which row n equals the inverse Binomial transform of column n of the triangle A034870 of even-indexed rows of Pascal's triangle.

1, 4, 10, 48, 116, 560, 1352, 6528, 15760, 76096, 183712, 887040, 2141504, 10340096, 24963200, 120532992, 290992384, 1405035520, 3392055808, 16378294272, 39540700160, 190919389184, 460920178688, 2225519493120, 5372879343616

Offset: 0

Paul D. Hanna, Oct 25 2004

nonn

			Sequence begins: {1*1, 2*2, 5*2, 12*4, 29*4, 70*8, 169*8, 408*16, ...}.

Index entries for linear recurrences with constant coefficients, signature (0, 12, 0, -4).

Cf. A099603, A099605, A034870, A000129.

a(n)=polcoeff((1+4*x-2*x^2)/(1-12*x^2+4*x^4)+x*O(x^n),n)

a(n) = Pell(n+1)*2^[(n+1)/2]. a(n) = 12*a(n-2) - 4*a(n-4) for n>=4. G.f.: (1+4*x-2*x^2)/(1-12*x^2+4*x^4).

A099607 Antidiagonal sums of triangle A099605, in which row n equals the inverse binomial transform of column n of the triangle A034870 of even-indexed rows of Pascal's triangle.

Original entry on oeis.org

1, 2, 3, 9, 21, 40, 100, 225, 482, 1119, 2513, 5565, 12636, 28376, 63481, 143118, 321483, 721413, 1622729, 3645740, 8188668, 18406009, 41355654, 92914375, 208799157, 469157625, 1054150840, 2368736000, 5322460497, 11959337226

Offset: 0

Paul D. Hanna, Oct 25 2004

nonn

Index entries for linear recurrences with constant coefficients, signature (0, 2, 6, 3, -2, -1).

Cf. A099604, A099605, A034870.

{a(n)=polcoeff((1+2*x+x^2-x^3)/(1-2*x^2-6*x^3-3*x^4+2*x^5+x^6)+x*O(x^n),n)}

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

cp's OEIS Frontend

A099606 Row sums of triangle A099605, in which row n equals the inverse Binomial transform of column n of the triangle A034870 of even-indexed rows of Pascal's triangle.

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