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.

A254362 a(n) = 3*2^n + 3^n + 6.

Original entry on oeis.org

10, 15, 27, 57, 135, 345, 927, 2577, 7335, 21225, 62127, 183297, 543735, 1618905, 4832127, 14447217, 43243335, 129533385, 388206927, 1163834337, 3489930135, 10466644665, 31393642527, 94168344657, 282479868135, 847389272745, 2542067154927, 7626000138177
Offset: 0

Views

Author

Luciano Ancora, Jan 29 2015

Keywords

Comments

This is the sequence of third terms of "third partial sums of m-th powers".
Is this 10 followed by A087719? [Bruno Berselli, Jan 30 2015]

Links

Crossrefs

Cf. A062709, A254363, A254364.

Programs

  • Mathematica
    Table[3 * 2^n + 3^n + 6, {n, 0, 29}] (* Alonso del Arte, Jan 29 2015 *)
LinearRecurrence[{6,-11,6},{10,15,27},30] (* Harvey P. Dale, Oct 11 2024 *)
  • PARI
    vector(30, n, n--; 3*2^n + 3^n + 6) \\ Colin Barker, Jan 30 2015

Formula

G.f.: -(47*x^2-45*x+10) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 30 2015
a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3). - Colin Barker, Jan 30 2015

A254363 a(n) = 4^n + 6*2^n + 3^(n+1) + 10.

Original entry on oeis.org

20, 35, 77, 203, 605, 1955, 6677, 23723, 86765, 324275, 1231877, 4738043, 18396125, 71940995, 282882677, 1116985163, 4424500685, 17568076115, 69883311077, 278367837083, 1109978272445, 4429440153635, 17686354389077, 70651224045803, 282322365983405, 1128441973997555, 4511225627508677, 18037276107243323, 72126226025905565
Offset: 0

Views

Author

Luciano Ancora, Jan 29 2015

Keywords

Comments

This is the sequence of fourth terms of "third partial sums of m-th powers".

Links

Crossrefs

Cf. A062709, A254362, A254364.

Programs

  • Mathematica
    Table[4^n + 6*2^n + 3^(n + 1) + 10, {n, 0, 28}] (* Michael De Vlieger, Jan 30 2015 *)
  • PARI
    vector(30, n, n--; 4^n + 6*2^n + 3^(n+1) + 10) \\ Colin Barker, Jan 30 2015

Formula

From Colin Barker, Jan 30 2015: (Start)
G.f.: -(342*x^3-427*x^2+165*x-20)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)).
a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n > 3. (End)
E.g.f.: exp(x)*(exp(3*x) + 3*exp(2*x) + 6*exp(x) + 10). - Elmo R. Oliveira, Sep 12 2024

A254463 a(n) = 15*2^n + 6*4^n + 10*3^n + 3*5^n + 6^n + 21.

Original entry on oeis.org

56, 126, 378, 1386, 5778, 26226, 126378, 636426, 3314178, 17714466, 96660378, 536249466, 3015243378, 17141522706, 98333399178, 568324150506, 3305074833378, 19319850386946, 113420243462778, 668241096915546, 3948892688324178, 23393955029043186, 138880128205091178
Offset: 0

Views

Author

Luciano Ancora, Jan 31 2015

Keywords

Comments

This is the sequence of sixth terms of "third partial sums of m-th powers".

Links

Crossrefs

Cf. A062709, A254362, A254363, A254364, A254464.

Programs

  • Mathematica
    Table[15 2^n + 6 4^n + 10 3^n + 3 5^n + 6^n + 21, {n, 0, 25}] (* Michael De Vlieger, Jan 31 2015 *)
  • PARI
    vector(30, n, n--; 15*2^n + 6*4^n + 10*3^n + 3*5^n + 6^n + 21) \\ Colin Barker, Jan 31 2015

Formula

From Colin Barker, Jan 31 2015: (Start)
G.f.: -2*(12276*x^5 - 20578*x^4 + 12831*x^3 - 3766*x^2 + 525*x - 28)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)).
a(n) = 21*a(n-1) - 175*a(n-2) + 735*a(n-3) - 1624*a(n-4) + 1764*a(n-5) - 720*a(n-6). (End)
E.g.f.: exp(x)*(exp(5*x) + 3*exp(4*x) + 6*exp(3*x) + 10*exp(2*x) + 15*exp(x) + 21). - Elmo R. Oliveira, Sep 16 2024

A254464 a(n) = 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28.

Original entry on oeis.org

84, 210, 714, 2982, 14178, 73470, 404634, 2331462, 13906578, 85232910, 533860554, 3403329942, 22012307778, 144090486750, 952693102074, 6352175272422, 42655384385778, 288161867586990, 1956674663089194, 13344181547374902, 91343993647708578, 627261876368085630
Offset: 0

Views

Author

Luciano Ancora, Jan 31 2015

Keywords

Comments

This is the sequence of seventh terms of "third partial sums of m-th powers".

Links

Crossrefs

Cf. A062709, A254362, A254363, A254364, A254463.

Programs

  • Mathematica
    Table[21 2^n + 10 4^n + 15 3^n + 3 6^n + 6 5^n + 7^n + 28, {n, 0, 24}] (* Michael De Vlieger, Jan 31 2015 *)
LinearRecurrence[{28,-322,1960,-6769,13132,-13068,5040},{84,210,714,2982,14178,73470,404634},30] (* Harvey P. Dale, May 17 2019 *)
  • PARI
    vector(30, n, n--; 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28) \\ Colin Barker, Jan 31 2015

Formula

From Colin Barker, Jan 31 2015: (Start)
G.f.: -6*(40188*x^6 - 74058*x^5 + 52931*x^4 - 19005*x^3 + 3647*x^2 - 357*x + 14)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)).
a(n) = 28*a(n-1) - 322*a(n-2) + 1960*a(n-3) - 6769*a(n-4) + 13132*a(n-5) - 13068*a(n-6) + 5040*a(n-7). (End)
E.g.f.: exp(x)*(exp(x)*(exp(5*x) + 3*exp(4*x) + 6*exp(3*x) + 10*exp(2*x) + 15*exp(x) + 21) + 28). - Elmo R. Oliveira, Sep 16 2024

A254465 a(n) = 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56.

Original entry on oeis.org

126, 252, 672, 2232, 8592, 36552, 166992, 804552, 4037712, 20923272, 111231312, 603667272, 3331889232, 18646768392, 105558814032, 603280840392, 3475274371152, 20152803339912, 117513698083152, 688425727971912, 4048693055291472, 23888489018765832, 141334996634766672, 838119509472869832
Offset: 0

Views

Author

Luciano Ancora, Jan 31 2015

Keywords

Comments

This is the sequence of sixth terms of "fourth partial sums of m-th powers".

Links

Crossrefs

Cf. A140504, A254365, A254366, A254367, A254466.

Programs

  • Mathematica
    Table[35 2^n + 10 4^n + 20 3^n + 4 5^n + 6^n + 56, {n, 0, 24}] (* Michael De Vlieger, Jan 31 2015 *)
LinearRecurrence[{21,-175,735,-1624,1764,-720},{126,252,672,2232,8592,36552},30] (* Harvey P. Dale, Aug 02 2024 *)
  • PARI
    vector(30, n, n--; 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56) \\ Colin Barker, Jan 31 2015

Formula

G.f.: -6*(10036*x^5 -16454*x^4 +10065*x^3 -2905*x^2 +399*x -21) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Jan 31 2015
a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - Colin Barker, Jan 31 2015

A254466 a(n) = 56*2^n + 20*4^n + 35*3^n + 4*6^n + 10*5^n + 7^n + 84.

Original entry on oeis.org

210, 462, 1386, 5214, 22770, 110022, 571626, 3136014, 17944290, 106156182, 645091866, 4006997214, 25344197010, 162737255142, 1058251916106, 6955456112814, 46130658756930, 308314670926902, 2074188361172346, 14032607275346814, 95392686703000050
Offset: 0

Views

Author

Luciano Ancora, Jan 31 2015

Keywords

Comments

This is the sequence of seventh terms of "fourth partial sums of m-th powers".

Links

Crossrefs

Cf. A140504, A254365, A254366, A254367, A254465.

Programs

  • Mathematica
    Table[56 2^n + 20 4^n + 35 3^n + 4 6^n + 10 5^n + 7^n + 84, {n, 0, 24}] (* Michael De Vlieger, Jan 31 2015 *)
  • PARI
    vector(30, n, n--; 56*2^n + 20*4^n + 35*3^n + 4*6^n + 10*5^n + 7^n + 84) \\ Colin Barker, Jan 31 2015

Formula

G.f.: -6*(110440*x^6 -199272*x^5 +139840*x^4 -49405*x^3 +9345*x^2 -903*x +35) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - Colin Barker, Jan 31 2015
a(n) = 28*a(n-1) -322*a(n-2) +1960*a(n-3) -6769*a(n-4) +13132*a(n-5) -13068*a(n-6) +5040*a(n-7). - Colin Barker, Jan 31 2015

A254467 a(n) = 15*4^n + 70*2^n + 35*3^n + 5^(n+1) + 6^n + 126.

Original entry on oeis.org

252, 462, 1122, 3432, 12342, 49632, 216342, 1001952, 4863462, 24500352, 127161462, 676195872, 3668030982, 20227217472, 113076824982, 639383508192, 3649985092902, 21003583828992, 121677813214902, 708891056106912, 4149610383537222
Offset: 0

Views

Author

Luciano Ancora, Jan 31 2015

Keywords

Comments

This is the sequence of sixth terms of "fifth partial sums of m-th powers".

Links

Crossrefs

Cf. A168614, A254368, A254369, A254370, A254468.

Programs

  • Mathematica
    Table[15×4^n+70×2^n+35×3^n+5^(n+1)+6^n+126, {n, 0, 25}] (* Michael De Vlieger, Jan 31 2015 *)
LinearRecurrence[{21,-175,735,-1624,1764,-720},{252,462,1122,3432,12342,49632},30] (* Harvey P. Dale, Jul 16 2018 *)
  • PARI
    vector(30, n, n--; 15*4^n + 70*2^n + 35*3^n + 5^(n+1) + 6^n + 126) \\ Colin Barker, Jan 31 2015

Formula

G.f.: -6*(21310*x^5 -34383*x^4 +20750*x^3 -5920*x^2 +805*x -42) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Jan 31 2015
a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - Colin Barker, Jan 31 2015

A254468 a(n) = 35*4^n + 126*2^n + 70*3^n + 15*5^n + 5*6^n + 7^n + 210.

Original entry on oeis.org

462, 924, 2508, 8646, 35112, 159654, 787968, 4137966, 22807752, 130656534, 772253328, 4683193086, 29012227992, 182964472614, 1171328741088, 7594839621006, 49780643849832, 329318254755894, 2195866174387248, 14741498331453726, 99542297086537272
Offset: 0

Views

Author

Luciano Ancora, Jan 31 2015

Keywords

Comments

This is the sequence of seventh terms of "fifth partial sums of m-th powers".

Links

Crossrefs

Cf. A168614, A254368, A254369, A254370, A254467.

Programs

  • Mathematica
    Table[35 4^n + 126 2^n + 70 3^n + 15 5^n + 5 6^n + 7^n + 210, {n, 0, 25}] (* Michael De Vlieger, Jan 31 2015 *)
LinearRecurrence[{28,-322,1960,-6769,13132,-13068,5040},{462,924,2508,8646,35112,159654,787968},30] (* Harvey P. Dale, Dec 29 2019 *)
  • PARI
    vector(30, n, n--; 35*4^n + 126*2^n + 70*3^n + 15*5^n + 5*6^n + 7^n + 210) \\ Colin Barker, Jan 31 2015

Formula

G.f.: -6*(259610*x^6 -461263*x^5 +319473*x^4 -111595*x^3 +20900*x^2 -2002*x +77) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)). - Colin Barker, Jan 31 2015
a(n) = 28*a(n-1) -322*a(n-2) +1960*a(n-3) -6769*a(n-4) +13132*a(n-5) -13068*a(n-6) +5040*a(n-7). - Colin Barker, Jan 31 2015
Showing 1-8 of 8 results.

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

Content is available under The OEIS End-User License Agreement.