A254365 -id:A254365 - cp's OEIS frontend

A254366 a(n) = 4^n + 102^n + 43^n + 20.

35, 56, 112, 272, 760, 2336, 7672, 26432, 94360, 346016, 1295032, 4923392, 18943960, 73568096, 287731192, 1131465152, 4467809560, 17697740576, 70271780152, 279532195712, 1113469251160, 4439908895456, 17717752225912, 70745400779072, 282604862628760

Offset: 0

Luciano Ancora, Jan 29 2015

This is the sequence of fourth terms of "fourth 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. A140504, A254365, A254367.

Table[4^n + 10*2^n + 4*3^n + 20, {n, 0, 28}] (* Michael De Vlieger, Jan 30 2015 *)

vector(30, n, n--; 4^n + 10*2^n + 4*3^n + 20) \\ Colin Barker, Jan 30 2015

G.f.: -(638*x^3-777*x^2+294*x-35) / ((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

A254367 a(n) = 52^(n+2) + 2^(2n+2) + 103^n + 5^n + 35.

Original entry on oeis.org

70, 126, 294, 846, 2814, 10326, 40614, 168126, 723534, 3208806, 14570934, 67417806, 316645854, 1505245686, 7225414854, 34956689886, 170199537774, 832952952966, 4093454620374, 20184631056366, 99800366967294, 494533989722646, 2454868429675494

Offset: 0

Luciano Ancora, Jan 30 2015

This is the sequence of fifth terms of "fourth 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 (15,-85,225,-274,120).

Cf. A140504, A254365, A254366.

[5*2^(n+2)+2^(2*n+2)+10*3^n+5^n+35: n in [0..30]]; // Vincenzo Librandi, Feb 02 2015

Table[5 2^(n + 2) + 2^(2 n + 2) + 10 3^n + 5^n + 35, {n, 0, 30}] (* Vincenzo Librandi, Feb 02 2015 *)

vector(30, n, n--; 5*2^(n+2) + 2^(2*n+2) + 10*3^n + 5^n + 35) \\ Colin Barker, Jan 30 2015

a(n) = 15*a(n-1)-85*a(n-2)+225*a(n-3)-274*a(n-4)+120*a(n-5). - Colin Barker, Jan 30 2015

G.f.: -2*(2972*x^4-4302*x^3+2177*x^2-462*x+35) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)). - Colin Barker, Jan 30 2015

A254465 a(n) = 352^n + 104^n + 203^n + 45^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

Luciano Ancora, Jan 31 2015

This is the sequence of sixth terms of "fourth 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. A140504, A254365, A254366, A254367, A254466.

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 *)

vector(30, n, n--; 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56) \\ Colin Barker, Jan 31 2015

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) = 562^n + 204^n + 353^n + 46^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

Luciano Ancora, Jan 31 2015

This is the sequence of seventh terms of "fourth 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. A140504, A254365, A254366, A254367, A254465.

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 *)

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

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

cp's OEIS Frontend

A254366 a(n) = 4^n + 10*2^n + 4*3^n + 20.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A254367 a(n) = 5*2^(n+2) + 2^(2n+2) + 10*3^n + 5^n + 35.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A254366 a(n) = 4^n + 102^n + 43^n + 20.

A254367 a(n) = 52^(n+2) + 2^(2n+2) + 103^n + 5^n + 35.

A254465 a(n) = 352^n + 104^n + 203^n + 45^n + 6^n + 56.

A254466 a(n) = 562^n + 204^n + 353^n + 46^n + 10*5^n + 7^n + 84.