cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A239649 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

Original entry on oeis.org

2, 4, 4, 8, 20, 10, 16, 92, 112, 22, 32, 418, 1182, 560, 50, 64, 1898, 12246, 13476, 2874, 114, 128, 8588, 127454, 320314, 158728, 14788, 258, 256, 38888, 1320102, 7629186, 8634040, 1864886, 75540, 586, 512, 175974, 13703468, 181039448, 471203608
Offset: 1

Views

Author

R. H. Hardin, Mar 23 2014

Keywords

Comments

Table starts
....2.......4..........8............16...............32...................64
....4......20.........92...........418.............1898.................8588
...10.....112.......1182.........12246...........127454..............1320102
...22.....560......13476........320314..........7629186............181039448
...50....2874.....158728.......8634040........471203608..........25594620082
..114...14788....1864886.....232304146......29007348454........3608789598890
..258...75540...21813374....6219477628....1778793691226......506611939408296
..586..387306..255830770..167002115382..109328664988704....71303275040032094
.1330.1983686.2997975560.4480024646968.6715782662219974.10028169382114414238

Examples

			Some solutions for n=3 k=4
..3..1..3..1....3..0..1..3....1..0..3..3....3..0..0..0....1..0..3..3
..2..1..2..0....2..1..1..2....1..0..3..3....2..0..3..0....1..3..2..0
..1..3..1..0....2..1..1..1....1..0..3..3....2..1..2..3....1..0..0..0

Links

Crossrefs

Column 1 is A078040
Row 1 is A000079

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
k=2: [order 10]
k=3: [order 35]
Empirical for row n:
n=1: a(n) = 2*a(n-1)
n=2: a(n) = 3*a(n-1) +12*a(n-2) -18*a(n-3) -29*a(n-4) +19*a(n-5) +38*a(n-6) +8*a(n-7)
n=3: [order 25]
n=4: [order 91]

A240381 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

2, 2, 4, 4, 10, 10, 4, 38, 44, 22, 8, 90, 330, 148, 50, 8, 366, 1494, 2066, 636, 114, 16, 878, 12234, 17550, 16994, 2430, 258, 16, 3606, 57722, 279886, 281186, 116030, 9648, 586, 32, 8666, 477574, 2545618, 8802558, 3502886, 884792, 37946, 1330, 32, 35602
Offset: 1

Views

Author

R. H. Hardin, Apr 04 2014

Keywords

Comments

Table starts
....2......2.........4............4.............8..............8.............16
....4.....10........38...........90...........366............878...........3606
...10.....44.......330.........1494.........12234..........57722.........477574
...22....148......2066........17550........279886........2545618.......41758418
...50....636.....16994.......281186.......8802558......157432290.....5145703760
..114...2430....116030......3502886.....207932244.....7149227810...457988195982
..258...9648....884792.....52375114....6169009514...422227556156.54164128056204
..586..37946...6273952....672652728..148090588518.19320096061230
.1330.149336..46648918...9771038498.4275011910288
.3018.588102.335571098.127878632630

Examples

			Some solutions for n=4 k=4
..1..3..1..3....3..1..1..3....3..1..3..1....3..1..3..1....1..3..1..3
..1..3..1..3....3..0..2..0....3..1..2..1....3..0..2..0....1..2..2..2
..1..2..1..1....3..2..0..2....3..2..2..2....1..0..0..0....1..2..0..0
..3..0..0..2....2..0..0..0....1..0..0..0....2..0..1..2....2..3..2..1

Links

Crossrefs

Column 1 is A078040
Row 1 is A016116(n+1)

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
k=2: [order 14] for n>15
Empirical for row n:
n=1: a(n) = 2*a(n-2)
n=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)
n=3: [order 48] for n>50

A077970 Expansion of 1/(1+x-2*x^2+2*x^3).

Original entry on oeis.org

1, -1, 3, -7, 15, -35, 79, -179, 407, -923, 2095, -4755, 10791, -24491, 55583, -126147, 286295, -649755, 1474639, -3346739, 7595527, -17238283, 39122815, -88790435, 201512631, -457339131, 1037945263, -2355648787, 5346217575, -12133405675, 27537138399, -62496384899, 141837473047
Offset: 0

Views

Author

N. J. A. Sloane, Nov 17 2002

Keywords

Links

Crossrefs

Cf. A077946, A078040.

Programs

  • GAP
    a:=[1,1,-3];; for n in [4..40] do a[n]:=-a[n-1]+2*a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 24 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1+x-2*x^2+2*x^3) )); // G. C. Greubel, Jun 24 2019
  • Mathematica
    CoefficientList[Series[1/(1+x-2x^2+2x^3),{x,0,40}],x] (* or *) LinearRecurrence[ {-1,2,-2},{1,-1,3},40] (* Harvey P. Dale, Sep 29 2018 *)
  • PARI
    Vec(1/(1+x-2*x^2+2*x^3)+O(x^40)) \\ Charles R Greathouse IV, Sep 26 2012
  • Sage
    (1/(1+x-2*x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 24 2019

Formula

a(n) = (-1)^n*A077946(n). - R. J. Mathar, Feb 28 2019
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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