A017509 -id:A017509 - cp's OEIS frontend

A017510 a(n) = (11*n + 10)^2.

100, 441, 1024, 1849, 2916, 4225, 5776, 7569, 9604, 11881, 14400, 17161, 20164, 23409, 26896, 30625, 34596, 38809, 43264, 47961, 52900, 58081, 63504, 69169, 75076, 81225, 87616, 94249, 101124, 108241, 115600, 123201, 131044, 139129, 147456, 156025, 164836, 173889, 183184, 192721

Offset: 0

N. J. A. Sloane

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Powers of the form (11*n+10)^m: A017509 (m=1), this sequence (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

List([0..40], n-> (11*n+10)^2); # G. C. Greubel, Oct 29 2019

[(11*n+10)^2: n in [0..40]]; // G. C. Greubel, Oct 29 2019

seq((11*n+10)^2, n=0..40); # G. C. Greubel, Oct 29 2019

(11*Range[0,40]+10)^2 (* or *) LinearRecurrence[{3,-3,1}, {100,441,1024}, 40] (* Harvey P. Dale, Mar 31 2016 *)

a(n)=(11*n+10)^2 \\ Charles R Greathouse IV, Jun 17 2017

[(11*n+10)^2 for n in (0..40)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (100 + 141*x + x^2)/(1-x)^3.
E.g.f.: (100 + 341*x + 121*x^2)*exp(x). (End)

A017511 a(n) = (11*n + 10)^3.

Original entry on oeis.org

1000, 9261, 32768, 79507, 157464, 274625, 438976, 658503, 941192, 1295029, 1728000, 2248091, 2863288, 3581577, 4410944, 5359375, 6434856, 7645373, 8998912, 10503459, 12167000, 13997521, 16003008, 18191447, 20570824, 23149125, 25934336, 28934443, 32157432

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 (4,-6,4,-1).

Cf. A000578, A017509.

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), this sequence (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

List([0..40], n-> (11*n+10)^3); # G. C. Greubel, Oct 29 2019

[(11*n+10)^3: n in [0..40]]; // Vincenzo Librandi, May 26 2016

seq((11*n+10)^3, n=0..40); # G. C. Greubel, Oct 29 2019

Table[(11 n + 10)^3, {n, 0, 40}] (* Vincenzo Librandi, May 26 2016 *)
(11*Range[40] -1)^3 (* G. C. Greubel, Oct 29 2019 *)

makelist((11*n+10)^3, n,0,40); /* Martin Ettl, Oct 21 2012 */

vector(41, n, (11*n-1)^3) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^3 for n in (0..40)] # G. C. Greubel, Oct 29 2019

G.f.: (1000 + 5261*x + 1724*x^2 + x^3)/(1-x)^4. - Vincenzo Librandi, May 26 2016
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), for n>3. - Vincenzo Librandi, May 26 2016
a(n) = A000578(A017509(n)). - Michel Marcus, May 26 2016
E.g.f.: (1000 + 8261*x + 7623*x^2 + 1331*x^3)*exp(x). - G. C. Greubel, Oct 29 2019

A017512 a(n) = (11*n + 10)^4.

Original entry on oeis.org

10000, 194481, 1048576, 3418801, 8503056, 17850625, 33362176, 57289761, 92236816, 141158161, 207360000, 294499921, 406586896, 547981281, 723394816, 937890625, 1196883216, 1506138481, 1871773696, 2300257521, 2798410000, 3373402561, 4032758016, 4784350561

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), this sequence (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

List([0..30], n-> (11*n+10)^4); # G. C. Greubel, Oct 29 2019

[(11*n+10)^4: n in [0..30]]; // G. C. Greubel, Oct 29 2019

A017512:=n->(11*n+10)^4: seq(A017512(n), n=0..30); # Wesley Ivan Hurt, Apr 11 2017

(11*Range[0,30]+10)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1}, {10000, 194481,1048576,3418801,8503056},30] (* Harvey P. Dale, Dec 24 2014 *)

vector(31, n, (11*n-1)^4) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^4 for n in (0..30)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (10000 + 144481*x + 176171*x^2 + 20731*x^3 + x^4)/(1-x)^5.
E.g.f.: (10000 + 184481*x + 334807*x^2 + 141086*x^3 + 14641*x^4)*exp(x). (End)

A017513 a(n) = (11*n + 10)^5.

Original entry on oeis.org

100000, 4084101, 33554432, 147008443, 459165024, 1160290625, 2535525376, 4984209207, 9039207968, 15386239549, 24883200000, 38579489651, 57735339232, 83841135993, 118636749824, 164130859375, 222620278176, 296709280757, 389328928768, 503756397099

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), this sequence (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

List([0..30], n-> (11*n+10)^5); # G. C. Greubel, Oct 29 2019

[(11*n+10)^5: n in [0..30]]; // Vincenzo Librandi, Jun 01 2016

seq((11*n+10)^5, n=0..30); # G. C. Greubel, Oct 29 2019

(11*Range[30] -1)^5 (* G. C. Greubel, Jun 01 2016 *)

vector(31, n, (11*n-1)^5) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^5 for n in (0..30)] # G. C. Greubel, Oct 29 2019

From Chai Wah Wu, May 31 2016: (Start)
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 5.
G.f.: (x^5 + 248826*x^4 + 4943366*x^3 + 10549826*x^2 + 3484101*x + 100000)/(x - 1)^6. (End)
E.g.f.: (100000 + 3984101*x + 12743115*x^2 + 9749575*x^3 + 2342560*x^4 + 161051*x^5)*exp(x). - G. C. Greubel, Jun 01 2016

A017514 a(n) = (11*n + 10)^6.

Original entry on oeis.org

1000000, 85766121, 1073741824, 6321363049, 24794911296, 75418890625, 192699928576, 433626201009, 885842380864, 1677100110841, 2985984000000, 5053913144281, 8198418170944, 12827693806929, 19456426971136

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), this sequence (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

List([0..20], n-> (11*n+10)^6); # G. C. Greubel, Oct 29 2019

[(11*n+10)^6: n in [0..20]]; // G. C. Greubel, Oct 29 2019

seq((11*n+10)^6, n=0..20); # G. C. Greubel, Oct 29 2019

(11*Range[0,20]+10)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1000000, 85766121,1073741824,6321363049,24794911296, 75418890625, 192699928576},20] (* Harvey P. Dale, Apr 21 2012 *)

makelist((11*n+10)^6,n,0,30); /* Martin Ettl, Oct 21 2012 */

vector(21, n, (11*n-1)^6) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^6 for n in (0..20)] # G. C. Greubel, Oct 29 2019

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(0)=1000000, a(1)=85766121, a(2)=1073741824, a(3)=6321363049, a(4)=24794911296, a(5)=75418890625, a(6)=192699928576. - Harvey P. Dale, Apr 21 2012
From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (1000000 + 78766121*x + 494378977*x^2 + 571258822*x^3 + 127134022*x^4 + 2985977*x^5 + x^6)/(1-x)^7.
E.g.f.: (1000000 + 84766121*x + 451604791*x^2 + 559405990*x^3 + 233743565*x^4 + 36236475*x^5 + 1771561*x^6)*exp(x). (End)

A017515 a(n) = (11*n + 10)^7.

Original entry on oeis.org

10000000, 1801088541, 34359738368, 271818611107, 1338925209984, 4902227890625, 14645194571776, 37725479487783, 86812553324672, 182803912081669, 358318080000000, 662062621900811, 1164175380274048

Offset: 0

N. J. A. Sloane

G. C. Greubel, 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).

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), this sequence (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

List([0..20], n-> (11*n+10)^7); # G. C. Greubel, Oct 29 2019

[(11*n+10)^7: n in [0..20]]; // G. C. Greubel, Oct 29 2019

seq((11*n+10)^7, n=0..20); # G. C. Greubel, Oct 29 2019

(11*Range[20] -1)^7 (* G. C. Greubel, Oct 29 2019 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{10000000,1801088541,34359738368,271818611107,1338925209984,4902227890625,14645194571776,37725479487783},20] (* Harvey P. Dale, Mar 24 2025 *)

vector(21, n, (11*n-1)^7) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^7 for n in (0..20)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (10000000 + 1721088541*x + 20231030040*x^2 + 46811183311*x^3 + 26288037136*x^4 + 3118171011*x^5 + 35831800*x^6 + x^7)/(1-x)^8.
E.g.f.: (10000000 + 1791088541*x + 15383780643*x^2 + 29022110271*x^3 + 18775618400*x^4 + 4926550090*x^5 + 533239861*x^6 + 19487171*x^7)*exp(x). (End)

A017516 a(n) = (11*n + 10)^8.

Original entry on oeis.org

100000000, 37822859361, 1099511627776, 11688200277601, 72301961339136, 318644812890625, 1113034787454976, 3282116715437121, 8507630225817856, 19925626416901921, 42998169600000000, 86730203469006241

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), this sequence (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

List([0..20], n-> (11*n+10)^8); # G. C. Greubel, Oct 29 2019

[(11*n+10)^8: n in [0..20]]; // G. C. Greubel, Oct 29 2019

seq((11*n+10)^8, n=0..20); # G. C. Greubel, Oct 29 2019

(11*Range[0,20]+10)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84, 36,-9,1}, {100000000,37822859361,1099511627776,11688200277601, 72301961339136, 318644812890625,1113034787454976,3282116715437121, 8507630225817856}, 20] (* Harvey P. Dale, Mar 28 2015 *)

vector(21, n, (11*n-1)^8) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^8 for n in (0..20)] # G. C. Greubel, Oct 29 2019

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - Harvey P. Dale, Mar 28 2015
From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (100000000 + 36922859361*x + 762705893527*x^2 + 3145818564613*x^3 + 3526057254339*x^4 + 1096474378339*x^5 + 74441150053*x^6 + 429981687*x^7 + x^8)/(1-x)^9.
E.g.f.: (100000000 + 37722859361*x + 511982954527*x^2 + 1417172328726*x^3 + 1333126606581*x^4 + 526757558250*x^5 + 94718280426*x^6 + 7561022348*x^7 + 214358881*x^8)*exp(x). (End)

A017517 a(n) = (11*n + 10)^9.

Original entry on oeis.org

1000000000, 794280046581, 35184372088832, 502592611936843, 3904305912313344, 20711912837890625, 84590643846578176, 285544154243029527, 833747762130149888, 2171893279442309389, 5159780352000000000

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), this sequence (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

List([0..20], n-> (11*n+10)^9); # G. C. Greubel, Oct 29 2019

[(11*n+10)^9: n in [0..20]]; // G. C. Greubel, Oct 29 2019

seq((11*n+10)^9, n=0..20); # G. C. Greubel, Oct 29 2019

(11*Range[20] -1)^9 (* G. C. Greubel, Oct 29 2019 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1000000000,794280046581,35184372088832,502592611936843,3904305912313344,20711912837890625,84590643846578176,285544154243029527,833747762130149888,2171893279442309389},20] (* Harvey P. Dale, Apr 02 2024 *)

makelist((11*n+10)^9,n,0,30); /* Martin Ettl, Oct 21 2012 */

vector(21, n, (11*n-1)^9) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^9 for n in (0..20)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (1000000000 + 784280046581*x + 27286571623022*x^2 + 186371493144668* x^3 + 366572931352634*x^4 + 229943411037290*x^5 + 42937656267554*x^6 + 1749554857988*x^7 + 5159780342*x^8 + x^9)/(1-x)^10.
E.g.f.: (1000000000 + 793280046581*x + 16798405997835*x^2 + 66570222635015* x^3 + 87577732371360*x^4 + 48903633958641*x^5 + 12992922453126*x^6 + 1699710028962*x^7 + 104178416166*x^8 + 2357947691*x^9)*exp(x). (End)

A017518 a(n) = (11*n + 10)^10.

Original entry on oeis.org

10000000000, 16679880978201, 1125899906842624, 21611482313284249, 210832519264920576, 1346274334462890625, 6428888932339941376, 24842341419143568849, 81707280688754689024, 236736367459211723401

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), this sequence (m=10), A017519 (m=11), A017520 (m=12).

List([0..20], n-> (11*n+10)^10); # G. C. Greubel, Oct 29 2019

[(11*n+10)^10: n in [0..20]]; // G. C. Greubel, Oct 29 2019

seq((11*n+10)^10, n=0..20); # G. C. Greubel, Oct 29 2019

(11Range[0,20]+10)^10 (* Harvey P. Dale, Jul 15 2017 *)

vector(21, n, (11*n-1)^10) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^10 for n in (0..20)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (10000000000 + 16569880978201*x + 942971216082413*x^2 + 10142326791816440*x^3 + 32281828333734992*x^4 + 35474405873171354*x^5 + 13610715373012154*x^6 + 1612091585741792*x^7 + 40745420207240*x^8 + 61917364213*x^9 + x^10)/(1-x)^11.
E.g.f.: (10000000000 + 16669880978201*x + 546275072443111*x^2 + 3047302039281830*x^3 + 5461469997038605*x^4 + 4142091263396625*x^5 + 1525402079982627*x^6 + 290796919504080*x^7 + 28906295102850*x^8 + 1402978876145*x^9 + 25937424601*x^10)*exp(x). (End)

A017519 a(n) = (11*n + 10)^11.

Original entry on oeis.org

100000000000, 350277500542221, 36028797018963968, 929293739471222707, 11384956040305711104, 87507831740087890625, 488595558857835544576, 2161283703465490489863, 8007313507497959524352, 25804264053054077850709

Offset: 0

N. J. A. Sloane

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).

Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), this sequence (m=11), A017520 (m=12).

List([0..20], n-> (11*n+10)^11); # G. C. Greubel, Oct 29 2019

[(11*n+10)^11: n in [0..20]]; // G. C. Greubel, Oct 29 2019

seq((11*n+10)^11, n=0..20); # G. C. Greubel, Oct 29 2019

(11*Range[0,20]+10)^11 (* Harvey P. Dale, Nov 22 2014 *)

vector(21, n, (11*n-1)^11) \\ G. C. Greubel, Oct 29 2019

[(11*n+10)^11 for n in (0..20)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (100000000000 + 349077500542221*x + 31832067012457316*x^2 + 520044490279441677*x^3 + 2534320219783371888*x^4 + 4468718880116382474* x^5 + 3020981097246519528*x^6 + 752734159745082834*x^7 + 58804165095530448*x^8 + 943893657465737*x^9 + 743008370676*x^10 + x^11)/(1-x)^12.
E.g.f.: (100000000000 + 350177500542221*x + 17664171008939763*x^2 + 137043013485992911*x^3 + 328439702272184800*x^4 + 329312102088205280*x^5 + 161493561976042527*x^6 + 42078754876663857*x^7 + 6031583034624180*x^8 + 470893943631155*x^9 + 18545258589715*x^10 + 285311670611*x^11)*exp(x). (End)

cp's OEIS Frontend

A017510 a(n) = (11*n + 10)^2.

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A017511 a(n) = (11*n + 10)^3.

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A017512 a(n) = (11*n + 10)^4.

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A017513 a(n) = (11*n + 10)^5.

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A017514 a(n) = (11*n + 10)^6.

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A017515 a(n) = (11*n + 10)^7.

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