A129392 -id:A129392 - cp's OEIS frontend

A129393 Row sums of A129392.

1, 5, -15, 29, -23, -43, 225, -499, 601, 197, -2991, 8189, -12599, 5045, 35265, -125971, 236857, -206683, -327375, 1808861, -4117079, 5115797, 1120929, -23825971, 66994201, -105678715, 49059345, 275536829, -1022847863, 1966396277, -1807797375, -2442192979, 14557768441

Offset: 0

Jonas Wallgren, Apr 13 2007

sign

Also a diagonal close to the top of A129392.

Index entries for linear recurrences with constant coefficients, signature (-2, -1, 4).

Cf. A129392.

CoefficientList[Series[(4x^2-7x-1)/((x-1)(4x^2+3x+1)),{x,0,40}],x] (* or *) LinearRecurrence[{-2,-1,4},{1,5,-15},40] (* Harvey P. Dale, Apr 01 2023 *)

Conjectures from Colin Barker, Oct 07 2015: (Start)
a(n) = -2*a(n-1) - a(n-2) + 4*a(n-3) for n>2.
G.f.: (4*x^2-7*x-1) / ((x-1)*(4*x^2+3*x+1)).
(End)

More terms from R. J. Mathar, Apr 30 2007

A129394 Triangle read by rows: T(r,c)=T(r,c-1)+T(r,c+1)+T(r-1,c-1).

Original entry on oeis.org

0, 1, 2, 1, 2, -5, -8, -5, 2, 3, 9, 4, 0, 4, 9, 3, 4, 19, 12, -16, -32, -16, 12, 19, 4, 5, -107, -116, -28, 76, 120, 76, -28, -116, -107, 5, 6, 287, 276, 96, -64, -132, -144, -132, -64, 96, 276, 287, 6, 7, -367, -380, -300, -196, 8, 268, 392, 268, 8, -196, -300, -380, -367, 7, 8, -245, -260, 352, 992, 940, 144, -804, -1216

Offset: 0

Jonas Wallgren, Apr 13 2007

Like A129392, except edge elements=0,1,2,3,4,5,...

R. J. Mathar, Comments on A129392, A129394 and A129396

Cf. A129392, A129395.

Corrected and extended by R. J. Mathar, Jan 17 2008

A129396 Triangle read by rows: T(r,c)=T(r,c-1)+T(r,c+1)+T(r-1,c-1).

Original entry on oeis.org

1, 2, 5, 2, 3, -10, -15, -10, 3, 4, 16, 9, 3, 9, 16, 4, 5, 22, 13, -25, -47, -25, 13, 22, 5, 6, -140, -151, -33, 105, 163, 105, -33, -151, -140, 6, 7, 378, 365, 127, -87, -181, -199, -181, -87, 127, 365, 378, 7, 8, -504, -519, -393, -239, 27, 353, 507, 353, 27, -239, -393, -519, -504, 8, 9, -194, -211, 487, 1217, 1123, 145

Offset: 0

Jonas Wallgren, Apr 13 2007

Like A129392, except edge elements=1,2,3,4,5...

R. J. Mathar, Comments on A129392, A129394 and A129396

Cf. A129392, A129397.

More terms from R. J. Mathar, Jan 17 2008

A129398 Pyramid P(h,x,y)=P(h,x,y-1)+P(h,x,y+1)+P(h,x-1,y)+P(h,x+1,y)+P(h-1,x,y), read level by level, x by x.

Original entry on oeis.org

1, 1, 1, 5, 1, 1, 1, 1, -3, 1, 1, -3, -7, -3, 1, 1, -3, 1, 1, 1, 1, 4, 1, 1, 3, 0, 3, 1, 1, 4, 0, -7, 0, 4, 1, 1, 3, 0, 3, 1, 1, 4, 1, 1

Offset: 0

Jonas Wallgren, Apr 13 2007

sign

All face elements=1. For an element x on a level inside the pyramid
..b
.cxd
..e
with a above x, x=a+b+c+d+e. Every level of the pyramid is symmetric. Thus the top (h=0) of the pyramid is 1. The level h=1 is
..1
.1.5.1
..1
The level h=2 is
.....1
..1.-3..1
1.-3.-7.-3..1
..1.-3..1
.....1
The level h=3 is
........1
.....1..4..1
..1..3..0..3..1
1..4..0.-7..0..4..1
..1..3..0..3..1
.....1..4..1
........1

This is a three-dimensional analog of A129392.

Cf. A129392, A129399.

cp's OEIS Frontend

A129393 Row sums of A129392.

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A129394 Triangle read by rows: T(r,c)=T(r,c-1)+T(r,c+1)+T(r-1,c-1).

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A129396 Triangle read by rows: T(r,c)=T(r,c-1)+T(r,c+1)+T(r-1,c-1).

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A129398 Pyramid P(h,x,y)=P(h,x,y-1)+P(h,x,y+1)+P(h,x-1,y)+P(h,x+1,y)+P(h-1,x,y), read level by level, x by x.

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