A001015 -id:A001015 - cp's OEIS frontend

A016915 a(n) = (6*n)^7.

0, 279936, 35831808, 612220032, 4586471424, 21870000000, 78364164096, 230539333248, 587068342272, 1338925209984, 2799360000000, 5455160701056, 10030613004288, 17565568854912, 29509034655744

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. A001015, A008588.

[(6*n)^7: n in [0..30]]; // Vincenzo Librandi, May 03 2011

(6*Range[0,20])^7 (* Harvey P. Dale, Jul 20 2011 *)

G.f.: (279936*(x + 120*x^2 + 1191*x^3 + 2416*x^4 + 1191*x^5 + 120*x^6 + x^7))/ (x-1)^8. - Harvey P. Dale, Jul 20 2011

A017095 a(n) = (8*n + 2)^7.

Original entry on oeis.org

128, 10000000, 612220032, 8031810176, 52523350144, 230539333248, 781250000000, 2207984167552, 5455160701056, 12151280273024, 24928547056768, 47829690000000, 86812553324672, 150363025899136, 250226879128704, 402271083010688, 627485170000000, 953133216331392, 1414067010444416

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, A016819, A017089 (8n+2), A001015 (n^7).

[(8*n+2)^7: n in [0..30]]; // Vincenzo Librandi, Jul 12 2011

Table[(8*n + 2)^7, {n, 0, 20}] (* Amiram Eldar, Apr 24 2023 *)

From Amiram Eldar, Apr 24 2023: (Start)
a(n) = A017089(n)^7.
a(n) = 2^7*A016819(n).
Sum_{n>=0} 1/a(n) = 61*Pi^7/47185920 + 127*zeta(7)/32768. (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

A017239 a(n) = (9*n + 6)^7.

Original entry on oeis.org

279936, 170859375, 4586471424, 42618442977, 230539333248, 897410677851, 2799360000000, 7446353252589, 17565568854912, 37725479487783, 75144747810816, 140710042265625, 250226879128704, 425927596977747

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 (n^7), A017233 (9*n+6).

[(9*n+6)^7: n in [0..25]]; // Vincenzo Librandi, Jul 25 2011

(9*Range[0,20]+6)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{279936,170859375,4586471424,42618442977,230539333248,897410677851,2799360000000,7446353252589},20] (* Harvey P. Dale, Feb 11 2015 *)

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8); a(0)=279936, a(1)=170859375, a(2)=4586471424, a(3)=42618442977, a(4)=230539333248, a(5)=897410677851, a(6)=2799360000000, a(7)=7446353252589. - Harvey P. Dale, Feb 11 2015

A017263 a(n) = (9*n + 8)^7.

Original entry on oeis.org

2097152, 410338673, 8031810176, 64339296875, 319277809664, 1174711139837, 3521614606208, 9095120158391, 20971520000000, 44231334895529, 86812553324672, 160578147647843, 282621973446656, 476837158203125, 775771085481344, 1222791080775407, 1874584905187328

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 (n^7), A017257 (9*n+8).

[(9*n+8)^7: n in [0..20]]; // Vincenzo Librandi, Jul 28 2011

(9*Range[0,20]+8)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{2097152,410338673,8031810176,64339296875,319277809664,1174711139837,3521614606208,9095120158391},30] (* Harvey P. Dale, Apr 06 2013 *)

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8); a(0)=2097152, a(1)=410338673, a(2)=8031810176, a(3)=64339296875, a(4)=319277809664, a(5)=1174711139837, a(6)=3521614606208, a(7)=9095120158391. - Harvey P. Dale, Apr 06 2013

More terms from Harvey P. Dale, Apr 06 2013

A017275 a(n) = (10*n)^7.

Original entry on oeis.org

0, 10000000, 1280000000, 21870000000, 163840000000, 781250000000, 2799360000000, 8235430000000, 20971520000000, 47829690000000, 100000000000000, 194871710000000, 358318080000000, 627485170000000

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, A008592.

[(10*n)^7: n in [0..20]]; // Vincenzo Librandi, Jul 29 2011

A017275:=n->(10*n)^7; seq(A017275(n), n=0..20); # Wesley Ivan Hurt, Feb 10 2014

Table[(10 n)^7, {n, 0, 20}] (* Wesley Ivan Hurt, Feb 10 2014 *)

a(n)=(10*n)^7 \\ Charles R Greathouse IV, Jul 29 2011

a(n) = (10n)^7 = A008592(n)^7 = A001015(A008592(n)). - Wesley Ivan Hurt, Feb 10 2014

A017323 a(n) = (10*n + 4)^7.

Original entry on oeis.org

16384, 105413504, 4586471424, 52523350144, 319277809664, 1338925209984, 4398046511104, 12151280273024, 29509034655744, 64847759419264, 131593177923584, 250226879128704, 450766669594624, 775771085481344

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, A017317.

[(10*n+4)^7: n in [0..20] ]; // Vincenzo Librandi, Aug 01 2011

A017323:=n->(10*n+4)^7: seq(A017323(n), n=0..30); # Wesley Ivan Hurt, Jan 28 2017

(10*Range[0,20]+4)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{16384,105413504,4586471424,52523350144,319277809664,1338925209984,4398046511104,12151280273024},20] (* Harvey P. Dale, Aug 26 2015 *)

a(n)=(10*n+4)^7 \\ Charles R Greathouse IV, Jan 29 2017

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8); a(0)=16384, a(1)=105413504, a(2)=4586471424, a(3)=52523350144, a(4)=319277809664, a(5)=1338925209984, a(6)=4398046511104, a(7)=12151280273024. - Harvey P. Dale, Aug 26 2015

A017395 a(n) = (11*n)^7.

Original entry on oeis.org

0, 19487171, 2494357888, 42618442977, 319277809664, 1522435234375, 5455160701056, 16048523266853, 40867559636992, 93206534790699, 194871710000000, 379749833583241, 698260569735168, 1222791080775407

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Cf. A001015, A008593.

[(11*n)^7: n in [0..30]]; // Vincenzo Librandi, May 03 2011

(11Range[0,20])^7 (* Harvey P. Dale, May 02 2011 *)

a(n) = A001015(A008593(n)). - Michel Marcus, Sep 03 2018

A017659 a(n) = (12n+11)^7.

Original entry on oeis.org

19487171, 3404825447, 64339296875, 506623120463, 2488651484819, 9095120158391, 27136050989627, 69833729609375, 160578147647843, 337931541778439, 662062621900811, 1222791080775407, 2149422977421875

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A001015, A017653.

[(12*n+11)^7: n in [0..15]]; // Vincenzo Librandi, May 21 2012

(12Range[0,20]+11)^7 (* Harvey P. Dale, May 16 2012 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{19487171,3404825447,64339296875,506623120463,2488651484819,9095120158391,27136050989627,69833729609375},20] (* Harvey P. Dale, May 16 2012 *)

a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)- 70*a(n-4)+ 56*a(n-5)- 28*a(n-6)+ 8*a(n-7)-a(n-8). - Harvey P. Dale, May 16 2012

a(n) = A001015(A017653(n)). - Michel Marcus, Oct 29 2022

A050754 Seventh powers containing no pair of consecutive equal digits.

Original entry on oeis.org

0, 1, 128, 2187, 16384, 78125, 823543, 2097152, 4782969, 19487171, 35831808, 62748517, 105413504, 170859375, 268435456, 893871739, 4586471424, 6103515625, 8031810176, 10460353203, 13492928512, 17249876309, 34359738368

Offset: 0

Patrick De Geest, Sep 15 1999

Cf. A043096, A001015, A050746.

cp's OEIS Frontend

A016915 a(n) = (6*n)^7.

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A017095 a(n) = (8*n + 2)^7.

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

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A017239 a(n) = (9*n + 6)^7.

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A017263 a(n) = (9*n + 8)^7.

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A017275 a(n) = (10*n)^7.

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A017323 a(n) = (10*n + 4)^7.

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A017395 a(n) = (11*n)^7.

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