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 1-10 of 36 results. Next

A325745 First term of n-th difference sequence of (floor(r*k)), r = (1+sqrt(5))/2, k >= 0.

Original entry on oeis.org

1, 1, -2, 4, -7, 10, -10, 0, 35, -125, 325, -725, 1451, -2639, 4355, -6435, 8255, -8567, 5863, -455, 910, -40105, 210418, -733447, 2085525, -5200299, 11748373, -24416951, 46909837, -82930835, 132479945, -182029055, 182029055, 1, -670853985, 2480588545
Offset: 1

Views

Author

Clark Kimberling, Jun 06 2019

Keywords

Links

Crossrefs

Cf. A001622, A325664. Inverse binomial transform of A000201.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[GoldenRatio*n], {n, 0, 50}], n]], {n, 2, 50}]

A325666 First term of n-th difference sequence of (floor(k*r)), r = sqrt(3), k >= 0.

Original entry on oeis.org

1, 1, -1, 0, 3, -9, 19, -35, 63, -119, 239, -495, 1023, -2079, 4158, -8239, 16247, -31823, 61402, -115291, 207669, -352715, 550429, -748143, 748143, 1, -2848367, 10897033, -30955333, 77558760, -181129041, 404458737, -875889377, 1855921144, -3870685665
Offset: 1

Views

Author

Clark Kimberling, May 13 2019

Keywords

Links

Crossrefs

Cf. A325664, A325667.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[Sqrt[3]*n], {n, 0, 50}], n]], {n, 1, 50}]

A325667 First term of n-th difference sequence of (floor(k*r)), r = -sqrt(3), k >= 0.

Original entry on oeis.org

-2, 0, 0, 1, -4, 10, -20, 36, -64, 120, -240, 496, -1024, 2080, -4159, 8240, -16248, 31824, -61403, 115292, -207670, 352716, -550430, 748144, -748144, 0, 2848366, -10897032, 30955332, -77558759, 181129040, -404458736, 875889376, -1855921143, 3870685664
Offset: 1

Views

Author

Clark Kimberling, May 13 2019

Keywords

Links

Crossrefs

Cf. A325664, A325666.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[-Sqrt[3]*n], {n, 0, 50}], n]], {n, 1, 50}]

A325668 First term of n-th difference sequence of (floor(k*r)), r = sqrt(5), k >= 0.

Original entry on oeis.org

2, 0, 0, 0, 1, -5, 15, -35, 71, -135, 255, -495, 991, -2015, 4095, -8255, 16511, -32895, 65535, -130815, 261630, -523753, 1048322, -2096151, 4183700, -8324849, 16480854, -32363019, 62784774, -119759849, 223346544, -404491999, 705032194, -1166803109
Offset: 1

Views

Author

Clark Kimberling, May 13 2019

Keywords

Links

Crossrefs

Cf. A325664, A325669.
Inverse binomial transform of A022839.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[Sqrt[5]*n], {n, 0, 50}], n]], {n, 1, 50}]

A325669 First term of n-th difference sequence of (floor(k*r)), r = -sqrt(5), k >= 0.

Original entry on oeis.org

-3, 1, -1, 1, -2, 6, -16, 36, -72, 136, -256, 496, -992, 2016, -4096, 8256, -16512, 32896, -65536, 130816, -261631, 523754, -1048323, 2096152, -4183701, 8324850, -16480855, 32363020, -62784775, 119759850, -223346545, 404492000, -705032195, 1166803110
Offset: 1

Views

Author

Clark Kimberling, May 13 2019

Keywords

Links

Crossrefs

Cf. A325664, A325668.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[-Sqrt[5]*n], {n, 0, 50}], n]], {n, 1, 50}]

A325670 First term of n-th difference sequence of (floor(k*r)), r = sqrt(6), k >= 0.

Original entry on oeis.org

2, 0, 1, -3, 7, -15, 31, -63, 127, -255, 510, -1011, 1968, -3717, 6720, -11439, 17874, -24309, 24309, 0, -92358, 352485, -997569, 2485242, -5754024, 12680955, -26924184, 55410642, -110821283, 215426355, -406270425, 740354804, -1294617072, 2145852303
Offset: 1

Views

Author

Clark Kimberling, May 13 2019

Keywords

Links

Crossrefs

Cf. A022840, A325664, A325671.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[Sqrt[6]*n], {n, 0, z}], n]], {n, 0, 50}]

A325671 First term of n-th difference sequence of (floor(k*r)), r = -sqrt(6), k >= 0.

Original entry on oeis.org

-3, 1, -2, 4, -8, 16, -32, 64, -128, 256, -511, 1012, -1969, 3718, -6721, 11440, -17875, 24310, -24310, 1, 92357, -352484, 997568, -2485241, 5754023, -12680954, 26924183, -55410641, 110821282, -215426354, 406270424, -740354803, 1294617071, -2145852302
Offset: 1

Views

Author

Clark Kimberling, May 15 2019

Keywords

Links

Crossrefs

Cf. A022840, A325664, A325670.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[-Sqrt[6]*n], {n, 0, 30}], n]], {n, 0, 50}]

A325672 First term of n-th difference sequence of (floor(k*r)), r = sqrt(7), k >= 0.

Original entry on oeis.org

2, 1, -2, 4, -7, 10, -10, 1, 26, -80, 161, -242, 242, 1, -730, 2188, -4376, 6580, -6733, 1140, 13718, -32945, 18920, 158356, -851599, 2896920, -8097220, 20058301, -45540944, 96506230, -193012459, 367077448, -667617643, 1166803110, -1968991970, 3225375253
Offset: 1

Views

Author

Clark Kimberling, May 15 2019

Keywords

Links

Crossrefs

Cf. A022841, A325664, A325673.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[Sqrt[7]*n], {n, 0, 30}], n]], {n, 0, 50}]

A325673 First term of n-th difference sequence of (floor(k*r)), r = -sqrt(7), k >= 0.

Original entry on oeis.org

-3, 0, 1, -3, 6, -9, 9, 0, -27, 81, -162, 243, -243, 0, 729, -2187, 4375, -6579, 6732, -1139, -13719, 32946, -18921, -158355, 851598, -2896919, 8097219, -20058300, 45540943, -96506229, 193012458, -367077447, 667617642, -1166803109, 1968991969, -3225375252
Offset: 1

Views

Author

Clark Kimberling, May 15 2019

Keywords

Links

Crossrefs

Cf. A022841, A325664, A325672.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[-Sqrt[7]*n], {n, 0, 30}], n]], {n, 0, 50}]

A325674 First term of n-th difference sequence of (floor(k*r)), r = sqrt(8), k >= 0.

Original entry on oeis.org

2, 1, -1, 1, -1, 0, 5, -20, 55, -125, 251, -462, 803, -1364, 2365, -4367, 8735, -18564, 40409, -87380, 184603, -379049, 758099, -1486674, 2884775, -5592404, 10919089, -21572459, 43144919, -87087000, 176565485, -357913940, 723002335, -1453179125, 2906358250
Offset: 1

Views

Author

Clark Kimberling, May 15 2019

Keywords

Links

Crossrefs

Cf. A022842, A325664, A325675.

Programs

  • Mathematica
    Table[First[Differences[Table[Floor[Sqrt[8]*n], {n, 0, 30}], n]], {n, 0, 50}]
Showing 1-10 of 36 results. Next

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