A016759 -id:A016759 - cp's OEIS frontend

A215960 First differences of A016759.

2186, 75938, 745418, 3959426, 14704202, 43261346, 108110858, 239479298, 483533066, 907216802, 1603736906, 2698690178, 4356837578, 6789523106, 10262737802, 15105828866, 21720853898, 30592580258, 42299129546, 57523267202, 77064337226, 101850842018

Offset: 0

N. J. A. Sloane, Aug 28 2012

Bruno Berselli, Table of n, a(n) for n = 0..1000
Philippe A. J. G. Chevalier, On the discrete geometry of physical quantities, Preprint, 2012.
Philippe A. J. G. Chevalier, A "table of Mendeleev" for physical quantities?, Slides from a talk, May 14 2014, Leuven, Belgium.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A016759.

[2*(7*t*(t*(t+17)+91)+1093) where t is 4*n*(n+2): n in [0..21]]; // Bruno Berselli, Aug 29 2012

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {2186, 75938, 745418, 3959426, 14704202, 43261346, 108110858}, 22] (* Bruno Berselli, Aug 29 2012 *)

G.f.: 2*(1093+30318*x+129879*x^2+129844*x^3+30339*x^4+1086*x^5+x^6)/(1-x)^7. [Bruno Berselli, Aug 29 2012]

a(n) = 2*(7*t*(t*(t+17)+91)+1093), where t=4*n*(n+2). [Bruno Berselli, Aug 29 2012]

A016951 a(n) = (6*n + 3)^7.

Original entry on oeis.org

2187, 4782969, 170859375, 1801088541, 10460353203, 42618442977, 137231006679, 373669453125, 897410677851, 1954897493193, 3938980639167, 7446353252589, 13348388671875, 22876792454961, 37725479487783, 60170087060757, 93206534790699, 140710042265625, 207616015289871

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A016759, A016945, A016946, A016947, A016948, A016949, A016950.

Subsequence of A001015.

[(6*n+3)^7: n in [0..40]]; // Vincenzo Librandi, May 05 2011

a[n_] := (6*n + 3)^7; Array[a, 50, 0] (* Amiram Eldar, Mar 30 2022 *)

From Amiram Eldar, Mar 30 2022: (Start)
a(n) = A016945(n)^7.
a(n) = 3^7*A016759(n).
Sum_{n>=0} 1/a(n) = 127*zeta(7)/279936.
Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/403107840. (End)

A016747 a(n) = (2*n)^7.

Original entry on oeis.org

0, 128, 16384, 279936, 2097152, 10000000, 35831808, 105413504, 268435456, 612220032, 1280000000, 2494357888, 4586471424, 8031810176, 13492928512, 21870000000, 34359738368, 52523350144, 78364164096, 114415582592, 163840000000, 230539333248, 319277809664, 435817657216

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A016759.

[(2*n)^7: n in [0..30]]; // Vincenzo Librandi, Sep 05 2011

A016747:=n->(2*n)^7: seq(A016747(n), n=0..40); # Wesley Ivan Hurt, Sep 15 2018

(2*Range[0,20])^7  (* Harvey P. Dale, Jan 17 2011 *)

vector(30, n, n--; (2*n)^7) \\ G. C. Greubel, Sep 15 2018

O.g.f.: 128*x*(1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1-x)^8. - R. J. Mathar, May 07 2008
From Amiram Eldar, Oct 10 2020: (Start)
Sum_{n>=1} 1/a(n) = zeta(7)/128.
Sum_{n>=1} (-1)^(n+1)/a(n) = 63*zeta(7)/8192. (End)

A016831 a(n) = (4n+2)^7.

Original entry on oeis.org

128, 279936, 10000000, 105413504, 612220032, 2494357888, 8031810176, 21870000000, 52523350144, 114415582592, 230539333248, 435817657216, 781250000000, 1338925209984, 2207984167552, 3521614606208, 5455160701056, 8235430000000, 12151280273024, 17565568854912, 24928547056768

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A013665, A016759, A016825.

Table[(4*n + 2)^7, {n, 0, 20}] (* Amiram Eldar, Apr 21 2023 *)

From Amiram Eldar, Apr 21 2023: (Start)
a(n) = A016825(n)^7.
a(n) = 2^7*A016759(n).
Sum_{n>=0} 1/a(n) = 127*zeta(7)/16384.
Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/23592960. (End)

A017119 a(n) = (8n + 4)^7 = 4^7(2*n + 1)^7.

Original entry on oeis.org

16384, 35831808, 1280000000, 13492928512, 78364164096, 319277809664, 1028071702528, 2799360000000, 6722988818432, 14645194571776, 29509034655744, 55784660123648, 100000000000000, 171382426877952, 282621973446656, 450766669594624, 698260569735168, 1054135040000000, 1555363874947072, 2248392813428736

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A001015, A013665, A016759, A016831, A017113.

[(8*n+4)^7: n in [0..20] ]; // Vincenzo Librandi, Jul 21 2011

A017119:=n->(8*n+4)^7; seq(A017119(n), n=0..20); # Wesley Ivan Hurt, Mar 10 2014

Table[(8*n+4)^7, {n, 0, 20}] (* Wesley Ivan Hurt, Mar 10 2014 *)

a(n) = (8*n+4)^7; \\ Michel Marcus, Mar 11 2014

a(n) = A001015(A017113(n)). - Wesley Ivan Hurt, Mar 10 2014
a(n) = 16384*A016759(n). - Michel Marcus, Mar 11 2014
G.f.: 16384*(x+1)*(x^6 + 2178*x^5 + 58479*x^4 + 201244*x^3 + 58479*x^2 + 2178*x + 1) / (x-1)^8. - Colin Barker, Mar 11 2014
From Amiram Eldar, Apr 25 2023: (Start)
a(n) = 2^7*A016831(n).
Sum_{n>=0} 1/a(n) = 127*zeta(7)/2097152.
Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/3019898880. (End)

More terms from Michel Marcus, Mar 11 2014

A017335 a(n) = (10*n + 5)^7.

Original entry on oeis.org

78125, 170859375, 6103515625, 64339296875, 373669453125, 1522435234375, 4902227890625, 13348388671875, 32057708828125, 69833729609375, 140710042265625, 266001988046875, 476837158203125, 817215093984375, 1347646586640625, 2149422977421875, 3329565857578125

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A013665, A016759, A017329.

[(10*n+5)^7: n in [0..25]]; // Vincenzo Librandi, Aug 02 2011

Table[(10*n + 5)^7, {n, 0, 20}] (* Amiram Eldar, Apr 18 2023 *)

G.f.: 78125*(x+1)*(x^6 + 2178*x^5 + 58479*x^4 + 201244*x^3 + 58479*x^2 + 2178*x + 1)/(x-1)^8. - Colin Barker, Nov 13 2012
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^7.
a(n) = 5^7 * A016759(n).
Sum_{n>=0} 1/a(n) = 127*zeta(7)/10000000.
Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/14400000000. (End)

cp's OEIS Frontend

A215960 First differences of A016759.

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Magma

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A016951 a(n) = (6*n + 3)^7.

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Magma

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A016747 a(n) = (2*n)^7.

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A016831 a(n) = (4n+2)^7.

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A017119 a(n) = (8*n + 4)^7 = 4^7*(2*n + 1)^7.

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Magma

Maple

Mathematica

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A017335 a(n) = (10*n + 5)^7.

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Author

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Magma

Mathematica

Formula

A017119 a(n) = (8n + 4)^7 = 4^7(2*n + 1)^7.