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 1-7 of 7 results.

A367243 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 2.

Original entry on oeis.org

0, 15, 91, 381, 1375, 4605, 14791, 46341, 142975, 436845, 1326391, 4010901, 12096175, 36415485, 109500391, 329009061, 988042975, 2966160525, 8902544791, 26715760821, 80163535375, 240523111965, 721634347591, 2165033066181, 6495359245375, 19486597829805, 58460833676791
Offset: 1

Views

Author

Stefano Spezia, Nov 11 2023

Keywords

Comments

a(n) is the number of n-digit numbers in A366959.

Links

Crossrefs

Cf. A366959.
Cf. A000079, A000244.
Cf. A367244, A367245, A367246, A367247, A367248, A367249, A367250.

Programs

  • Mathematica
    LinearRecurrence[{6,-11,6},{0,15,91},27]

Formula

a(n) = (46*3^n - 93*2^n + 48)/6.
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 3.
O.g.f.: x^2*(15 + x)/((1 - x)*(1- 2*x)*(1 - 3*x)).
E.g.f.: (exp(x) - 1)^2*(46*exp(x) - 1)/6.

A367244 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 3.

Original entry on oeis.org

0, 13, 119, 733, 3815, 18133, 81599, 354493, 1504055, 6278053, 25904879, 106011853, 431253095, 1746686773, 7051884959, 28403182813, 114200118935, 458563556293, 1839545301839, 7374058107373, 29543870469575, 118318410678613, 473702458475519, 1896096339905533, 7588244995073015
Offset: 1

Views

Author

Stefano Spezia, Nov 11 2023

Keywords

Comments

a(n) is the number of n-digit numbers in A366960.

Links

Crossrefs

Cf. A366960.
Cf. A000079, A000244, A000302.
Cf. A367243, A367245, A367246, A367247, A367248, A367249, A367250.

Programs

  • Mathematica
    LinearRecurrence[{9,-26,24},{0,13,119},25]

Formula

a(n) = 27*4^(n-1) - 41*3^(n-1) + 7*2^n.
a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3) for n > 3.
O.g.f.: x^2*(13 + 2*x)/((1 - 2*x)*(1 - 3*x)*(1 - 4*x)).
E.g.f.: (exp(x) - 1)^2*(81*exp(2*x) - 2*exp(x) - 1)/12.

A367245 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 4.

Original entry on oeis.org

0, 11, 135, 1103, 7551, 46871, 273735, 1534943, 8366031, 44674151, 234982935, 1222071983, 6301114911, 32274971831, 164471580135, 834802180223, 4223960206191, 21320114811911, 107403378865335, 540232762595663, 2714041233191871, 13621757688226391, 68315120054438535
Offset: 1

Views

Author

Stefano Spezia, Nov 11 2023

Keywords

Comments

a(n) is the number of n-digit numbers in A366961.

Links

Crossrefs

Cf. A366961.
Cf. A000244, A000302, A000351.
Cf. A367243, A367244, A367246, A367247, A367248, A367249, A367250.

Programs

  • Mathematica
    LinearRecurrence[{12,-47,60},{0,11,135},23]

Formula

a(n) = 29*5^(n-1) - 47*4^(n-1) + 2*3^(n+1).
a(n) = 12*a(n-1) - 47*a(n-2) + 60*a(n-3) for n > 3.
O.g.f.: x^2*(11 + 3*x)/((1 - 3*x)*(1 - 4*x)*(1 - 5*x)).
E.g.f.: (116*exp(5*x) - 235*exp(4*x) + 120*exp(3*x) - 1)/20.

A367246 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 5.

Original entry on oeis.org

0, 9, 139, 1419, 12079, 92859, 669319, 4617699, 30878959, 201792939, 1295974999, 8212422579, 51499341439, 320287850619, 1978857202279, 12161478061059, 74421280021519, 453832688077899, 2759692966903159, 16742329188365139, 101377580843991199, 612894508749226779, 3700556151386869639
Offset: 1

Views

Author

Stefano Spezia, Nov 11 2023

Keywords

Comments

a(n) is the number of n-digit numbers in A366962.

Links

Crossrefs

Cf. A366962.
Cf. A000302, A000351, A000400.
Cf. A367243, A367244, A367245, A367247, A367248, A367249, A367250.

Programs

  • Mathematica
    LinearRecurrence[{15,-74,120},{0,9,139},23]

Formula

a(n) = 29*6^(n-1) - 49*5^(n-1) + 5*4^n.
a(n) = 15*a(n-1) - 74*a(n-2) + 120*a(n-3) for n > 3.
O.g.f.: x^2*(9 + 4*x)/((1 - 4*x)*(1 - 5*x)*(1 - 6*x)).
E.g.f.: (145*exp(6*x) - 294*exp(5*x) + 150*exp(4*x) - 1)/30.

A367247 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 6.

Original entry on oeis.org

0, 7, 131, 1609, 16415, 150817, 1296191, 10641169, 84520175, 654958177, 4980233951, 37312922929, 276288797135, 2026564724737, 14750977566911, 106695818055889, 767748717541295, 5500729672814497, 39270143125479071, 279511731951144049, 1984459091985376655, 14059238393314971457
Offset: 1

Views

Author

Stefano Spezia, Nov 11 2023

Keywords

Comments

a(n) is the number of n-digit numbers in A366963.

Links

Crossrefs

Cf. A366963.
Cf. A000351, A000400, A000420.
Cf. A367243, A367244, A367245, A367246, A367248, A367249, A367250.

Programs

  • Mathematica
    LinearRecurrence[{18,-107,210},{0,7,131},22]

Formula

a(n) = 27*7^(n-1) - 47*6^(n-1) + 4*5^n.
a(n) = 21*a(n-1) - 146*a(n-2) + 336*a(n-3) for n > 3.
O.g.f.: x^2*(7 + 5*x)/((1 - 5*x)*(1 - 6*x)*(1 - 7*x)).
E.g.f.: (162*exp(7*x) - 329*exp(6*x) + 168*exp(5*x) - 1)/42.

A367248 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 7.

Original entry on oeis.org

0, 5, 111, 1601, 19095, 204545, 2045511, 19508081, 179752215, 1613908385, 14202967911, 123028446161, 1052237271735, 8907026785025, 74758478722311, 623053865857841, 5162154289325655, 42558224511290465, 349394287423788711, 2858263098464575121, 23311522539676521975
Offset: 1

Views

Author

Stefano Spezia, Nov 11 2023

Keywords

Comments

a(n) is the number of n-digit numbers in A366964.

Links

Crossrefs

Cf. A366964.
Cf. A000400, A000420, A001018.
Cf. A367243, A367244, A367245, A367246, A367247, A367249, A367250.

Programs

  • Mathematica
    LinearRecurrence[{21,-146,336},{0,5,111},21]

Formula

a(n) = 23*8^(n-1) - 41*7^(n-1) + 3*6^n.
a(n) = 21*a(n-1) - 146*a(n-2) + 336*a(n-3) for n > 3.
O.g.f.: x^2*(5 + 6*x)/((1 - 6*x)*(1 - 7*x)*(1 - 8*x)).
E.g.f.: (161*exp(8*x) - 328*exp(7*x) + 168*exp(6*x) - 1)/56.

A367249 a(n) is the number of n-digit numbers whose difference between the largest and smallest digits is equal to 8.

Original entry on oeis.org

0, 3, 79, 1323, 18175, 223323, 2555119, 27828363, 292407775, 2990349243, 29943991759, 294872615403, 2864776362175, 27525734996763, 262061152909999, 2475899571994443, 23240879960425375, 216963121865909883, 2015960236625789839, 18656492902684557483, 172056837889322101375
Offset: 1

Views

Author

Stefano Spezia, Nov 11 2023

Keywords

Comments

a(n) is the number of n-digit numbers in A366965.

Links

Crossrefs

Cf. A366965.
Cf. A000420, A001018, A001019.
Cf. A367243, A367244, A367245, A367246, A367247, A367248, A367250.

Programs

  • Mathematica
    LinearRecurrence[{24,-191,504},{0,3,79},21]

Formula

a(n) = 17*9^(n-1) - 31*8^(n-1) + 2*7^n.
a(n) = 24*a(n-1) - 191*a(n-2) + 504*a(n-3) for n > 3.
O.g.f.: x^2*(3 + 7*x)/((1 - 7*x)*(1 - 8*x)*(1 - 9*x)).
E.g.f.: (136*exp(9*x) - 279*exp(8*x) + 144*exp(7*x) - 1)/72.
Showing 1-7 of 7 results.

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