A254370 -id:A254370 - cp's OEIS frontend

A254368 a(n) = 5*2^n + 3^n + 15.

21, 28, 44, 82, 176, 418, 1064, 2842, 7856, 22258, 64184, 187402, 551936, 1635298, 4864904, 14512762, 43374416, 129795538, 388731224, 1164882922, 3492027296, 10470838978, 31402031144, 94185121882, 282513422576, 847456381618, 2542201372664, 7626268573642, 22878134632256, 68633061719458, 205896500803784, 617684133702202

Offset: 0

Luciano Ancora, Jan 29 2015

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

Colin Barker, Table of n, a(n) for n = 0..1000
Luciano Ancora, Demonstration of formulas, page 1.
Luciano Ancora, Recurrence relations for partial sums of m-th powers
Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Cf. A168614, A254369, A254370.

Table[5 2^n + 3^n + 15, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)
LinearRecurrence[{6,-11,6},{21,28,44},40] (* Harvey P. Dale, Apr 26 2022 *)

vector(30, n, n--; 5*2^n + 3^n + 15) \\ Colin Barker, Jan 30 2015

G.f.: -(107*x^2-98*x+21) / ((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

A254369 a(n) = 152^n + 4^n + 53^n + 35.

Original entry on oeis.org

56, 84, 156, 354, 936, 2754, 8736, 29274, 102216, 368274, 1359216, 5110794, 19495896, 75203394, 292596096, 1145977914, 4511183976, 17827536114, 70660511376, 280697078634, 1116961278456, 4450379734434, 17749154257056, 70839585900954, 282887376051336, 1130136853206354, 4516309963145136, 18052528510172874, 72171982026734616

Offset: 0

Luciano Ancora, Jan 29 2015

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

Colin Barker, Table of n, a(n) for n = 0..1000
Luciano Ancora, Demonstration of formulas, page 2.
Luciano Ancora, Recurrence relations for partial sums of m-th powers
Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Cf. A168614, A254368, A254370.

Table[15 2^n + 4^n + 5 3^n + 35, {n, 0, 30}] (* Bruno Berselli, Jan 30 2015 *)
LinearRecurrence[{10,-35,50,-24},{56,84,156,354},30] (* Harvey P. Dale, Dec 04 2020 *)

vector(30, n, n--; 15*2^n + 4^n + 5*3^n + 35) \\ Colin Barker, Jan 30 2015

G.f.: -2*(533*x^3-638*x^2+238*x-28) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Jan 30 2015

a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - Colin Barker, Jan 30 2015

A254467 a(n) = 154^n + 702^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

Luciano Ancora, Jan 31 2015

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

Colin Barker, Table of n, a(n) for n = 0..1000
Luciano Ancora, Demonstration of formulas, page 2.
Luciano Ancora, Recurrence relations for partial sums of m-th powers
Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).

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

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 *)

vector(30, n, n--; 15*4^n + 70*2^n + 35*3^n + 5^(n+1) + 6^n + 126) \\ Colin Barker, Jan 31 2015

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) = 354^n + 1262^n + 703^n + 155^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

Luciano Ancora, Jan 31 2015

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

Colin Barker, Table of n, a(n) for n = 0..1000
Luciano Ancora, Demonstration of formulas, page 2.
Luciano Ancora, Recurrence relations for partial sums of m-th powers
Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).

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

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 *)

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

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

cp's OEIS Frontend

A254368 a(n) = 5*2^n + 3^n + 15.

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Formula

A254369 a(n) = 15*2^n + 4^n + 5*3^n + 35.

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Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A254369 a(n) = 152^n + 4^n + 53^n + 35.

A254467 a(n) = 154^n + 702^n + 35*3^n + 5^(n+1) + 6^n + 126.

A254468 a(n) = 354^n + 1262^n + 703^n + 155^n + 5*6^n + 7^n + 210.