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 1-8 of 8 results.

A279780 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 8/5.

Original entry on oeis.org

1, -3, 5, -9, 17, -30, 52, -90, 154, -262, 446, -758, 1286, -2182, 3702, -6278, 10646, -18054, 30614, -51910, 88022, -149254, 253078, -429126, 727638, -1233798, 2092054, -3547334, 6014934, -10199046, 17293718, -29323590, 49721686, -84309126, 142956310
Offset: 0

Views

Author

Clark Kimberling, Dec 18 2016

Keywords

Comments

If n > 4, then a(n) is even.

Links

Crossrefs

Cf. A279634, A279778, A279779, A279781, A289260.

Programs

  • Mathematica
    z = 50; f[x_] := f[x] = Sum[Floor[(8/5)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]

Formula

G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 8/5.
G.f.: (1 - x) (1 - x^5)/(1 + 2 x + x^2 + 2 x^3 + 2 x^4).

A279676 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 5/3.

Original entry on oeis.org

1, -3, 4, -3, -1, 8, -14, 12, 4, -32, 56, -48, -16, 128, -224, 192, 64, -512, 896, -768, -256, 2048, -3584, 3072, 1024, -8192, 14336, -12288, -4096, 32768, -57344, 49152, 16384, -131072, 229376, -196608, -65536, 524288, -917504, 786432, 262144, -2097152
Offset: 0

Views

Author

Clark Kimberling, Dec 18 2016

Keywords

Comments

If n >=11, then 16 divides a(n).

Links

Crossrefs

Cf. A279634, A279675.

Programs

  • Mathematica
    z = 50; f[x_] := f[x] = Sum[Floor[(5/3)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]

Formula

G.f.: 1/(1 + 2x + 4x^2 + 5x^3 + 6x^4 + 8x^5 + ...).
G.f.: (1 - x) (1 - x^3)/(1 + 2 x + 2 x^2).

A279778 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 6/5.

Original entry on oeis.org

1, -2, 1, 0, -1, 3, -3, 1, 1, -5, 9, -7, 1, 7, -19, 25, -15, -5, 33, -63, 65, -25, -43, 129, -191, 155, -7, -215, 449, -537, 317, 201, -879, 1435, -1391, 433, 1281, -3193, 4261, -3215, -415, 5755, -10647, 11737, -6015, -6585, 22157, -33031, 29489, -5445
Offset: 0

Views

Author

Clark Kimberling, Dec 18 2016

Keywords

Links

Crossrefs

Cf. A279634, A279779, A279780, A279781.

Programs

  • Mathematica
    z = 50; f[x_] := f[x] = Sum[Floor[(6/5)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]
LinearRecurrence[{-1,-1,-1,-2},{1,-2,0,-1,3,-3},50] (* Harvey P. Dale, Mar 11 2024 *)

Formula

G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 6/5.
G.f.: (1 - x) (1 - x^5)/(1 + x + x^2 + x^3 + 2 x^4).

A279779 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 7/5.

Original entry on oeis.org

1, -2, 0, 3, -3, 0, 4, -7, 5, 5, -16, 15, 2, -26, 39, -19, -37, 88, -73, -28, 160, -207, 61, 249, -484, 339, 258, -950, 1063, -99, -1593, 2628, -1469, -1996, 5492, -5287, -763, 9837, -14008, 5671, 14034, -31042, 25319, 11389, -59053, 73040, -16961, -92844
Offset: 0

Views

Author

Clark Kimberling, Dec 18 2016

Keywords

Links

Crossrefs

Cf. A279634, A279778, A279780, A279781.

Programs

  • Mathematica
    z = 50; f[x_] := f[x] = Sum[Floor[(7/5)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]

Formula

G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 7/5.
G.f.: (1 - x) (1 - x^5)/(1 + x + 2 x^2 + x^3 + 2 x^4).

A279781 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 9/5.

Original entry on oeis.org

1, -3, 4, -4, 4, -3, -1, 8, -16, 24, -30, 28, -12, -20, 68, -128, 184, -208, 168, -32, -224, 592, -1008, 1344, -1408, 960, 224, -2240, 4928, -7744, 9664, -9216, 4736, 5120, -20608, 39936, -58368, 67840, -57600, 16384, 63488, -180224, 315904, -431104, 463872
Offset: 0

Views

Author

Clark Kimberling, Dec 18 2016

Keywords

Comments

If n >= 23, then 32 divides a(n).

Links

Crossrefs

Cf. A279634, A279778, A279779, A279780.

Programs

  • Mathematica
    z = 50; f[x_] := f[x] = Sum[Floor[(9/5)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]
LinearRecurrence[{-2,-2,-2,-2},{1,-3,4,-4,4,-3,-1},50] (* Harvey P. Dale, Jul 07 2025 *)

Formula

G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 9/5.
G.f.: (1 - x) (1 - x^5)/(1 + 2 x + 2 x^2 + 2 x^3 + 2 x^4).

A279675 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 4/3.

Original entry on oeis.org

1, -2, 0, 3, -2, -4, 8, 0, -16, 16, 16, -48, 16, 80, -112, -48, 272, -176, -368, 720, 16, -1456, 1424, 1488, -4336, 1360, 7312, -10032, -4592, 24656, -15472, -33840, 64784, 2896, -132464, 126672, 138256, -391600, 115088, 668112, -898288, -437936, 2234512
Offset: 0

Views

Author

Clark Kimberling, Dec 18 2016

Keywords

Comments

If n >=7, then 16 divides a(n).

Links

Crossrefs

Cf. A279634, A279676.

Programs

  • Mathematica
    z = 50; f[x_] := f[x] = Sum[Floor[(4/3)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]

Formula

G.f.: 1/(1 + 2x + 4x^2 + 5x^3 + 6x^4 + 8x^5 + ...).
G.f.: (1 - x) (1 - x^3)/(1 + x + 2 x^2).

A279677 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 5/4.

Original entry on oeis.org

1, -2, 1, -1, 3, -3, 2, -5, 9, -8, 9, -19, 26, -25, 37, -64, 77, -87, 138, -205, 241, -312, 481, -651, 794, -1105, 1613, -2096, 2693, -3823, 5322, -6885, 9209, -12968, 17529, -22979, 31386, -43465, 58037, -77344, 106237, -144967, 193418, -260925, 357441
Offset: 0

Views

Author

Clark Kimberling, Dec 18 2016

Keywords

Links

Crossrefs

Cf. A279634, A279678.

Programs

  • Mathematica
    z = 50; f[x_] := f[x] = Sum[Floor[(5/4)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]

Formula

G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 5/4.
G.f.: (1 - x) (1 - x^4)/(1 + x + x^2 + 2 x^3).

A279678 Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 7/4.

Original entry on oeis.org

1, -3, 4, -4, 5, -9, 16, -24, 34, -52, 84, -132, 200, -304, 472, -736, 1136, -1744, 2688, -4160, 6432, -9920, 15296, -23616, 36480, -56320, 86912, -134144, 207104, -319744, 493568, -761856, 1176064, -1815552, 2802688, -4326400, 6678528, -10309632, 15915008
Offset: 0

Views

Author

Clark Kimberling, Dec 18 2016

Keywords

Comments

If n >=18, then 32 divides a(n).

Links

Crossrefs

Cf. A279634, A279677.

Programs

  • Mathematica
    z = 50; f[x_] := f[x] = Sum[Floor[(7/4)*(k + 1)] x^k, {k, 0, z}]; f[x]
CoefficientList[Series[1/f[x], {x, 0, z}], x]

Formula

G.f.: 1/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = 7/4.
G.f.: (1 - x) (1 - x^4)/(1 + 2 x + 2 x^2 + 2 x^3).
Showing 1-8 of 8 results.

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

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