A008455 -id:A008455 - cp's OEIS frontend

A168627 a(n) = n^6*(n^5 + 1)/2.

0, 1, 1056, 88938, 2099200, 24421875, 181421856, 988722196, 4295098368, 15690795525, 50000500000, 142656721086, 371505678336, 896082610423, 2024786349600, 4324883625000, 8796101410816, 17135960222601

Offset: 0

N. J. A. Sloane, Dec 11 2009

nonn

Number of unoriented rows of length 11 using up to n colors. For a(0)=0, there are no rows using no colors. For a(1)=1, there is one row using that one color for all positions. For a(2)=1056, there are 2^11=2048 oriented arrangements of two colors. Of these, 2^6=64 are achiral. That leaves (2048-64)/2=992 chiral pairs. Adding achiral and chiral, we get 1056. - Robert A. Russell, Nov 13 2018

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Row 11 of A277504.

Cf. A008455 (oriented), A001014 (achiral).

List([0..30], n -> n^6*(1 + n^5)/2); # G. C. Greubel, Nov 15 2018

[n^6*(1 + n^5)/2: n in [0..30]]; // G. C. Greubel, Nov 15 2018

Table[n^6*(n^5+1)/2, {n, 0, 30}] (* G. C. Greubel, Jul 27 2016 *)
LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{0,1,1056,88938,2099200,24421875,181421856,988722196,4295098368,15690795525,50000500000,142656721086},20] (* Harvey P. Dale, Nov 21 2024 *)

vector(30, n, n--; n^6*(1 + n^5)/2) \\ G. C. Greubel, Nov 15 2018

[n^6*(1 + n^5)/2 for n in range(30)] # G. C. Greubel, Nov 15 2018

From G. C. Greubel, Jul 27 2016: (Start)
G.f.: x*(1 + 1044*x + 76332*x^2 + 1101420*x^3 + 4869558*x^4 + 7862124*x^5 + 4868556*x^6 + 1102068*x^7 + 76305*x^8 + 992*x^9)/(1 - x)^12.
E.g.f.: (1/2)* x *(2 + 1054*x + 28591*x^2 + 145815*x^3 + 246745*x^4 + 179488*x^5 + 63987*x^6 + 11880*x^7 + 1155*x^8 + 55*x^9 + x^10)*exp(x). (End)
From Robert A. Russell, Nov 13 2018: (Start)
a(n) = (A008455(n) + A001014(n)) / 2 = (n^11 + n^6) / 2.
G.f.: (Sum_{j=1..11} S2(11,j)*j!*x^j/(1-x)^(j+1) + Sum_{j=1..6} S2(6,j)*j!*x^j/(1-x)^(j+1)) / 2, where S2 is the Stirling subset number A008277.
G.f.: x*Sum_{k=0..10} A145882(11,k) * x^k / (1-x)^12.
E.g.f.: (Sum_{k=1..11} S2(11,k)*x^k + Sum_{k=1..6} S2(6,k)*x^k) * exp(x) / 2, where S2 is the Stirling subset number A008277.
For n>11, a(n) = Sum_{j=1..12} -binomial(j-13,j) * a(n-j). (End)

A004908 Numbers that are the sum of at most 2 positive 11th powers.

Original entry on oeis.org

0, 1, 2, 2048, 2049, 4096, 177147, 177148, 179195, 354294, 4194304, 4194305, 4196352, 4371451, 8388608, 48828125, 48828126, 48830173, 49005272, 53022429, 97656250, 362797056, 362797057, 362799104, 362974203, 366991360, 411625181

Offset: 1

N. J. A. Sloane

nonn

Zhuorui He, Table of n, a(n) for n = 1..10000

Cf. A008455 (11th powers), A004813 (sum of 2).

lista(nn) = setbinop((x,y)->x^11+y^11, [0..nn]); \\ Michel Marcus, Jul 02 2025

A016775 (3*n)^11.

Original entry on oeis.org

0, 177147, 362797056, 31381059609, 743008370688, 8649755859375, 64268410079232, 350277500542221, 1521681143169024, 5559060566555523, 17714700000000000, 50542106513726817, 131621703842267136, 317475837322472439, 717368321110468608

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 (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A008455 (11th Powers), A008585 (3n).

[(3*n)^11: n in [0..20]]; // Vincenzo Librandi, May 09 2011

A016775:=n->(3*n)^11: seq(A016775(n), n=0..20); # Wesley Ivan Hurt, Oct 28 2014

(3 Range[0, 20])^11 (* or *)
CoefficientList[Series[177147 (x + 2036 x^2 + 152637 x^3 + 2203488 x^4 + 9738114 x^5 + 15724248 x^6 + 9738114 x^7 + 2203488 x^8 + 152637 x^9 + 2036 x^10 + x^11)/(x - 1)^12, {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 28 2014 *)

A016775(n):=(3*n)^11$
makelist(A016775(n),n,0,20); /* Martin Ettl, Nov 12 2012 */

From Wesley Ivan Hurt, Oct 28 2014: (Start)
G.f.: 177147*(x + 2036*x^2 + 152637*x^3 + 2203488*x^4 + 9738114*x^5 + 15724248*x^6 + 9738114*x^7 + 2203488*x^8 + 152637*x^9 + 2036*x^10 + x^11) / (x - 1)^12.
a(n) = 12*a(n-1)-66*a(n-2)+220*a(n-3)-495*a(n-4)+792*a(n-5)-924*a(n-6)+792*a(n-7)-495*a(n-8)+220*a(n-9)-66*a(n-10)+12*a(n-11)-a(n-12).
a(n) = (3*n)^11 = 177147 * A008455(n) = A008455(A008585(n)). (End)

A016919 a(n) = (6*n)^11.

Original entry on oeis.org

0, 362797056, 743008370688, 64268410079232, 1521681143169024, 17714700000000000, 131621703842267136, 717368321110468608, 3116402981210161152, 11384956040305711104, 36279705600000000000

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 (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Cf. A008455, A008588.

[(6*n)^11: n in [0..25]]; // Vincenzo Librandi, May 03 2011

(6*Range[0,20])^11 (* Harvey P. Dale, Dec 22 2013 *)

a(x) = 362797056*(x-1)*(x^10 - 10*x^9 + 45*x^8 - 120*x^7 + 210*x^6 - 252*x^5 + 210*x^4 - 120*x^3 + 45*x^2 - 10*x + 1). - Harvey P. Dale, Dec 22 2013

A017087 a(n) = (8*n + 1)^11.

Original entry on oeis.org

1, 31381059609, 34271896307633, 2384185791015625, 50542106513726817, 550329031716248441, 3909821048582988049, 20635899893042801193, 87507831740087890625, 313726685568359708377, 984770902183611232881

Offset: 0

N. J. A. Sloane

Composition of A008455(n) and A017077(n). - Wesley Ivan Hurt, Jul 17 2025

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Cf. A008455, A017077.

[(8*n+1)^11: n in [0..20]]; // Vincenzo Librandi, Jul 11 2011

(8*Range[0,10]+1)^11 (* or *) LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,31381059609,34271896307633,2384185791015625,50542106513726817,550329031716248441,3909821048582988049,20635899893042801193,87507831740087890625,313726685568359708377,984770902183611232881,2775173073766990340489},20] (* Harvey P. Dale, Sep 08 2017 *)
CoefficientList[Series[(1 + 31381059597*x + 33895323592391*x^2 + 1974994185258003*x^3 + 24186918344729610*x^4 + 93655732195384290*x^5 + 134070558743608110*x^6 + 73557591075608934*x^7 + 14545208676272997*x^8 + 849143191166465*x^9 + 8626027938459*x^10 + 1977326743*x^11)/(-1 + x)^12, {x, 0, 15}], x] (* Wesley Ivan Hurt, Jul 17 2025 *)

a(n)=(8*n+1)^11 \\ Charles R Greathouse IV, Aug 11 2014

From Wesley Ivan Hurt, Jul 17 2025: (Start)
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12).
G.f.: (1 + 31381059597*x + 33895323592391*x^2 + 1974994185258003*x^3 +24186918344729610*x^4 + 93655732195384290*x^5 + 134070558743608110*x^6 + 73557591075608934*x^7 + 14545208676272997*x^8 + 849143191166465*x^9 + 8626027938459*x^10 + 1977326743*x^11)/(-1 + x)^12.
a(n) = A008455(A017077(n)). (End)

A017171 a(n) = (9*n)^11.

Original entry on oeis.org

0, 31381059609, 64268410079232, 5559060566555523, 131621703842267136, 1532278301220703125, 11384956040305711104, 62050608388552823487, 269561249468963094528, 984770902183611232881, 3138105960900000000000

Offset: 0

N. J. A. Sloane

Composition of A008455(n) and A008591(n). - Wesley Ivan Hurt, Jul 17 2025

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Cf. A008455, A008591.

[(9*n)^11: n in [0..15]]; // Vincenzo Librandi, Jul 22 2011

(9*Range[0,20])^11 (* Harvey P. Dale, Apr 06 2019 *)
CoefficientList[Series[31381059609*x*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10)/(-1 + x)^12, {x, 0, 15}], x] (* Wesley Ivan Hurt, Jul 17 2025 *)

a(n) = 31381059609*A008455(n). - R. J. Mathar, Jul 07 2017
From Wesley Ivan Hurt, Jul 17 2025: (Start)
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12).
G.f.: 31381059609*x*(1 + 2036*x + 152637*x^2 + 2203488*x^3 + 9738114*x^4 + 15724248*x^5 + 9738114*x^6 + 2203488*x^7 + 152637*x^8 + 2036*x^9 + x^10)/(-1 + x)^12.
a(n) = A008455(A008591(n)). (End)

A017267 a(n) = (9*n + 8)^11.

Original entry on oeis.org

8589934592, 34271896307633, 3670344486987776, 96549157373046875, 1196683881290399744, 9269035929372191597, 52036560683837093888, 231122292121701565271, 858993459200000000000, 2775173073766990340489

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 (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Cf. A008455 (n^11), A017257 (9*n+8).

[(9*n+8)^11: n in [0..10]]; // Vincenzo Librandi, Jul 28 2011

(9*Range[0,30]+8)^11 (* or *) LinearRecurrence[ {12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{8589934592,34271896307633,3670344486987776,96549157373046875,1196683881290399744,9269035929372191597,52036560683837093888,231122292121701565271,858993459200000000000,2775173073766990340489,8007313507497959524352,21048519522998348950643},30] (* Harvey P. Dale, Oct 21 2013 *)

a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12); a(0)=8589934592, a(1)=34271896307633, a(2)=3670344486987776, a(3)=96549157373046875, a(4)=1196683881290399744, a(5)=9269035929372191597, a(6)=52036560683837093888, a(7)=231122292121701565271, a(8)=858993459200000000000, a(9)=2775173073766990340489, a(10)=8007313507497959524352, a(11)=21048519522998348950643. - Harvey P. Dale, Oct 21 2013

A017291 a(n) = (10*n + 1)^11.

Original entry on oeis.org

1, 285311670611, 350277500542221, 25408476896404831, 550329031716248441, 6071163615208263051, 43513917611435838661, 231122292121701565271, 984770902183611232881, 3543686674874777831491, 11156683466653165551101

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 (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Cf. A008455 (n^11), A017281 (10n+1).

[(10*n+1)^11: n in [0..20]]; // Vincenzo Librandi, May 15 2011

(10Range[0,20]+1)^11 (* Harvey P. Dale, May 11 2011 *)

A017543 a(n) = (12*n + 1)^11.

Original entry on oeis.org

1, 1792160394037, 2384185791015625, 177917621779460413, 3909821048582988049, 43513917611435838661, 313726685568359708377, 1673432436896142578125, 7153014030880804126753, 25804264053054077850709, 81402749386839761113321, 230339304218442143770717

Offset: 0

N. J. A. Sloane

Matthew House, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Cf. A008455 (n^11), A017533 (12n+1).

[(12*n+1)^11: n in [0..12]]; // Vincenzo Librandi, Jul 29 2015

seq((12*n+1)^11, n=0..100); # Robert Israel, Jul 28 2015

vector(20, n, n--; (12*n+1)^11) \\ Michel Marcus, Jul 28 2015

a(n) = A008455(A017533(n)). - Michel Marcus, Jul 28 2015

a(n) = Sum_{k=0..11} binomial(11,k)*(12*n)^k. - Robert Israel, Jul 28 2015

A017627 a(n) = (12*n+8)^11.

Original entry on oeis.org

8589934592, 204800000000000, 36028797018963968, 1196683881290399744, 16985107389382393856, 143746751770690322432, 858993459200000000000, 3996373778857415671808, 15394540563150776827904, 51172646912339021398016

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 (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Cf. A008455, A017617.

[(12*n+8)^11: n in [0..20]]; // Vincenzo Librandi, Apr 19 2017

A017627:=n->(12*n+8)^11: seq(A017627(n), n=0..20); # Wesley Ivan Hurt, Apr 18 2017

Table[(12 n + 8)^11, {n, 0, 30}] (* Vincenzo Librandi, Apr 19 2017 *)

a(n) = A008455(A017617(n)). - Michel Marcus, Apr 19 2017

cp's OEIS Frontend

A168627 a(n) = n^6*(n^5 + 1)/2.

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A004908 Numbers that are the sum of at most 2 positive 11th powers.

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A016775 (3*n)^11.

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Maxima

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A016919 a(n) = (6*n)^11.

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A017087 a(n) = (8*n + 1)^11.

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A017171 a(n) = (9*n)^11.

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Magma

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A017267 a(n) = (9*n + 8)^11.

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Magma

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A017291 a(n) = (10*n + 1)^11.

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