A097474 -id:A097474 - cp's OEIS frontend

A097749 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows. Let A(n,k) be the triangle in A097474. Then T(n,k) is defined by the orthogonality relations Sum_{j=i..r} T(r,j)A(j,i)2^-floor((j+3)/2) = 0 if i != r, = (2r+1)!/(r!*2^r) if i = r.

2, 1, 2, -1, 10, 6, 5, -35, 105, 30, -63, 420, -882, 1260, 210, 1576, -10395, 20790, -20790, 17325, 1890, -68409, 450450, -891891, 849420, -495495, 270270, 20790, 4729726, -31126095, 61486425, -57972915, 32207175, -12297285, 4729725, 270270

Offset: 0

N. J. A. Sloane, Sep 21 2004

			Triangle begins:
2
1 2
-1 10 6
5 -35 105 30
-63 420 -882 1260 210

H. W. Gould, Power sum identities for arbitrary symmetric arrays, SIAM J. Appl. Math., 17 (1969), 307-316.

Cf. A097474, A097801. Row sums give A001147. Is the left-hand edge A004193?

More terms from Sean A. Irvine, Mar 25 2013

A097716 Left-hand edge of triangle in A097474.

Original entry on oeis.org

1, -1, 2, -17, 124, -2764, 43688, -1859138, 51236656, -3550889296, 151107728672, -15494138893232, 941930695305664, -133994296272170944, 11024086088089751168, -2077570618897716831248, 222290021402867410844416, -53603997631397508980982016, 7234385689981722178901729792

Offset: 0

N. J. A. Sloane, Sep 21 2004

More terms from Emeric Deutsch, Dec 24 2004

A097578 a(n) = (2n+1)2^floor((n+1)/2).

Original entry on oeis.org

1, 6, 10, 28, 36, 88, 104, 240, 272, 608, 672, 1472, 1600, 3456, 3712, 7936, 8448, 17920, 18944, 39936, 41984, 88064, 92160, 192512, 200704, 417792, 434176, 901120, 933888, 1933312, 1998848, 4128768, 4259840, 8781824, 9043968, 18612224, 19136512, 39321600

Offset: 0

N. J. A. Sloane, Sep 21 2004

nonn

Robert Israel, Table of n, a(n) for n = 0..6608
Index entries for linear recurrences with constant coefficients, signature (0,4,0,-4).

Right-hand edge of triangle in A097474.

seq(seq((4*k+2*j+1)*2^(k+j), j=[0,1]),k=0..50); # Robert Israel, Feb 28 2017

LinearRecurrence[{0,4,0,-4},{1,6,10,28},40] (* Harvey P. Dale, Sep 08 2021 *)

G.f.: (1+6*x+6*x^2+4*x^3)/(1-2*x^2)^2. - Robert Israel, Feb 28 2017

cp's OEIS Frontend

A097749 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows. Let A(n,k) be the triangle in A097474. Then T(n,k) is defined by the orthogonality relations Sum_{j=i..r} T(r,j)A(j,i)2^-floor((j+3)/2) = 0 if i != r, = (2r+1)!/(r!*2^r) if i = r.

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A097716 Left-hand edge of triangle in A097474.

Views

Author

Keywords

Extensions

A097578 a(n) = (2n+1)2^floor((n+1)/2).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Formula

cp's OEIS Frontend

A097749 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows. Let A(n,k) be the triangle in A097474. Then T(n,k) is defined by the orthogonality relations Sum_{j=i..r} T(r,j)*A(j,i)*2^-floor((j+3)/2) = 0 if i != r, = (2r+1)!/(r!*2^r) if i = r.

Views

Author

Keywords

Examples

References

Crossrefs

Extensions

A097716 Left-hand edge of triangle in A097474.

Views

Author

Keywords

Extensions

A097578 a(n) = (2*n+1)*2^floor((n+1)/2).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A097749 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows. Let A(n,k) be the triangle in A097474. Then T(n,k) is defined by the orthogonality relations Sum_{j=i..r} T(r,j)A(j,i)2^-floor((j+3)/2) = 0 if i != r, = (2r+1)!/(r!*2^r) if i = r.

A097578 a(n) = (2n+1)2^floor((n+1)/2).