A017468 -id:A017468 - cp's OEIS frontend

A017461 a(n) = 11*n + 6.

6, 17, 28, 39, 50, 61, 72, 83, 94, 105, 116, 127, 138, 149, 160, 171, 182, 193, 204, 215, 226, 237, 248, 259, 270, 281, 292, 303, 314, 325, 336, 347, 358, 369, 380, 391, 402, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 523, 534, 545, 556, 567, 578, 589

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017401, A017449, A141694.
Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.
Powers of the form (11*n+6)^m: this sequence (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

List([0..60], n-> 11*n+6); # G. C. Greubel, Sep 19 2019

[11*n+6: n in [0..60]]; // Vincenzo Librandi, Sep 03 2011

seq(11*n+6, n=0..60); # G. C. Greubel, Sep 19 2019

Range[6, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
LinearRecurrence[{2,-1},{6,17},60] (* or *) NestList[11 + #&, 6, 60] (* Harvey P. Dale, Apr 14 2015 *)

a(n)=11*n+6 \\ Charles R Greathouse IV, Oct 07 2015

[11*n+6 for n in (0..60)] # G. C. Greubel, Sep 19 2019

a(0)=6, a(1)=17; for n>1, a(n) = 2*a(n-1) - a(n-2). - Harvey P. Dale, Apr 14 2015
From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (6 + 5*x)/(1-x)^2.
E.g.f.: (6 + 11*x)*exp(x). (End)
a(n) = A141694(n)/2. - Elmo R. Oliveira, Apr 11 2025

A017462 a(n) = (11*n + 6)^2.

Original entry on oeis.org

36, 289, 784, 1521, 2500, 3721, 5184, 6889, 8836, 11025, 13456, 16129, 19044, 22201, 25600, 29241, 33124, 37249, 41616, 46225, 51076, 56169, 61504, 67081, 72900, 78961, 85264, 91809, 98596, 105625, 112896, 120409, 128164, 136161, 144400, 152881, 161604, 170569

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 (3,-3,1).

Powers of the form (11*n+6)^m: A017461 (m=1), this sequence (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

List([0..50], n-> (11*n+6)^2); # G. C. Greubel, Sep 19 2019

[(11*n+6)^2: n in [0..40]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+6)^2, n=0..50); # G. C. Greubel, Sep 19 2019

(11*Range[0,30]+6)^2 (* or *) LinearRecurrence[{3,-3,1},{36,289,784},30] (* Harvey P. Dale, Sep 24 2016 *)

a(n)=(11*n+6)^2 \\ Charles R Greathouse IV, Jun 17 2017

[(11*n+6)^2 for n in (0..50)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (36 +181*x +25*x^2)/(1-x)^3.
E.g.f.: (36 +253*x +121*x^2)*exp(x). (End)

A017463 a(n) = (11*n + 6)^3.

Original entry on oeis.org

216, 4913, 21952, 59319, 125000, 226981, 373248, 571787, 830584, 1157625, 1560896, 2048383, 2628072, 3307949, 4096000, 5000211, 6028568, 7189057, 8489664, 9938375, 11543176, 13312053, 15252992, 17373979, 19683000, 22188041, 24897088, 27818127, 30959144

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

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), this sequence (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

List([0..40], n-> (11*n+6)^3); # G. C. Greubel, Sep 19 2019

[(11*n+6)^3: n in [0..40]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+6)^3, n=0..40); # G. C. Greubel, Sep 19 2019

(* From Harvey P. Dale, May 16 2012 : (Start) *)
(11Range[0,40]+6)^3
LinearRecurrence[{4,-6,4,-1}, {216,4913, 21952,59319}, 40] (* End *)

vector(40, n, (11*n-5)^3) \\ G. C. Greubel, Sep 19 2019

[(11*n+6)^3 for n in (0..40)] # G. C. Greubel, Sep 19 2019

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=216, a(1)=4913, a(2)=21952, a(3)=59319. - Harvey P. Dale, May 16 2012
From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (216 +4049*x +3596*x^2 +125*x^3)/(1-x)^4.
E.g.f.: (216 +4697*x +6171*x^2 +1331*x^3)*exp(x). (End)

A017464 a(n) = (11*n + 6)^4.

Original entry on oeis.org

1296, 83521, 614656, 2313441, 6250000, 13845841, 26873856, 47458321, 78074896, 121550625, 181063936, 260144641, 362673936, 492884401, 655360000, 855036081, 1097199376, 1387488001, 1731891456, 2136750625, 2608757776, 3154956561, 3782742016, 4499860561, 5314410000

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 (5,-10,10,-5,1).

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), this sequence (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

List([0..30], n-> (11*n+6)^4); # G. C. Greubel, Sep 19 2019

[(11*n+6)^4: n in [0..30]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+6)^4, n=0..30); # G. C. Greubel, Sep 19 2019

(11*Range[30] -5)^4 (* G. C. Greubel, Sep 19 2019 *)
LinearRecurrence[{5,-10,10,-5,1},{1296,83521,614656,2313441,6250000},30] (* Harvey P. Dale, Oct 11 2021 *)

vector(30, n, (11*n-5)^4) \\ G. C. Greubel, Sep 19 2019

[(11*n+5)^4 for n in (0..30)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (1296 +77041*x +210011*x^2 +62411*x^3 +625*x^4)/(1-x)^5.
E.g.f.: (1296 +82225*x +224455*x^2 +119790*x^3 +14641*x^4)*exp(x). (End)

A017465 a(n) = (11*n + 6)^5.

Original entry on oeis.org

7776, 1419857, 17210368, 90224199, 312500000, 844596301, 1934917632, 3939040643, 7339040224, 12762815625, 21003416576, 33038369407, 50049003168, 73439775749, 104857600000, 146211169851, 199690286432, 267785184193, 353305857024, 459401384375, 589579257376

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 (6,-15,20,-15,6,-1).

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), this sequence (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

List([0..30], n-> (11*n+6)^5); # G. C. Greubel, Sep 19 2019

[(11*n+6)^5: n in [0..30]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+6)^5, n=0..30); # G. C. Greubel, Sep 19 2019

(11*Range[30] -5)^5 (* G. C. Greubel, Sep 19 2019 *)

vector(30, n, (11*n-5)^5) \\ G. C. Greubel, Sep 19 2019

[(11*n+6)^5 for n in (0..30)] # G. C. Greubel, Sep 19 2019

G.f.: (7776 +1373201*x +8807866*x^2 +8104326*x^3 +1029826*x^4 +3125*x^5 )/(1-x)^6. - Colin Barker, Sep 17 2012

E.g.f.: (7776 +1412081*x +7189215*x^2 +7140815*x^3 +2049740*x^4 + 161051*x^5)*exp(x). - G. C. Greubel, Sep 19 2019

A017466 a(n) = (11*n + 6)^6.

Original entry on oeis.org

46656, 24137569, 481890304, 3518743761, 15625000000, 51520374361, 139314069504, 326940373369, 689869781056, 1340095640625, 2436396322816, 4195872914689, 6906762437184, 10942526586601, 16777216000000, 25002110044521, 36343632130624, 51682540549249, 72074394832896

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 (7,-21,35,-35,21,-7,1).

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), this sequence (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

List([0..20], n-> (11*n+6)^6); # G. C. Greubel, Sep 19 2019

[(11*n+6)^6: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+6)^6, n=0..20); # G. C. Greubel, Sep 19 2019

(11 * Range[0, 20] + 6)^6 (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {46656, 24137569, 481890304, 3518743761, 15625000000, 51520374361, 139314069504}, 20] (* Harvey P. Dale, Jan 19 2013 *)

a(n)=(11*n+6)^6 \\ Charles R Greathouse IV, Nov 04 2017

[(11*n+6)^6 for n in (0..20)] # G. C. Greubel, Sep 19 2019

a(0) = 46656, a(1) = 24137569, a(2) = 481890304, a(3) = 3518743761, a(4) = 15625000000, a(5) = 51520374361, a(6) = 139314069504, 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). - Harvey P. Dale, Jan 19 2013
From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (46656 +23810977*x +313907097*x^2 +650767622*x^3 +270308102*x^4 +16667841*x^5 +15625*x^6)/(1-x)^7.
E.g.f.: (46656 +24090913*x +216830911*x^2 +357573150*x^3 +181035965*x^4 +32371251*x^5 +1771561*x^6)*exp(x). (End)

A017467 a(n) = (11*n + 6)^7.

Original entry on oeis.org

279936, 410338673, 13492928512, 137231006679, 781250000000, 3142742836021, 10030613004288, 27136050989627, 64847759419264, 140710042265625, 282621973446656, 532875860165503, 953133216331392, 1630436461403549, 2684354560000000, 4275360817613091, 6614541047773568

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).

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), this sequence (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

List([0..20], n-> (11*n+6)^7); # G. C. Greubel, Sep 19 2019

[(11*n+6)^7: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+6)^7, n=0..20); # G. C. Greubel, Sep 19 2019

(11 Range[0, 19] + 6)^7 (* Alonso del Arte, Nov 04 2017 *)

vector(20, n, (11*n-5)^7) \\ G. C. Greubel, Sep 19 2019

[(11*n+6)^7 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (279936 +408099185*x +10218057336*x^2 +40761385011*x^3 +38244574736 *x^4 +8315057055*x^5 +267810456*x^6 +78125*x^7)/(1-x)^8.
E.g.f.: (279936 +410058737*x +6336265551*x^2 +16330492871*x^3 + 12985102900*x^4 +3966041926*x^5 +483636153*x^6 +19487171*x^7)*exp(x). (End)

A017469 a(n) = (11*n + 6)^9.

Original entry on oeis.org

10077696, 118587876497, 10578455953408, 208728361158759, 1953125000000000, 11694146092834141, 51998697814228992, 186940255267540403, 572994802228616704, 1551328215978515625, 3802961274698203136

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), this sequence (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

List([0..20], n-> (11*n+6)^9); # G. C. Greubel, Sep 19 2019

[(11*n+6)^9: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+6)^9, n=0..20); # G. C. Greubel, Sep 19 2019

(11*Range[0,20]+6)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210, 120,-45,10,-1}, {10077696, 118587876497,10578455953408, 208728361158759, 1953125000000000,11694146092834141,51998697814228992,186940255267540403, 572994802228616704, 1551328215978515625}, 20] (* Harvey P. Dale, Jan 15 2019 *)

vector(20, n, (11*n-5)^9) \\ G. C. Greubel, Sep 19 2019

[(11*n+6)^9 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (10077696 +118487099537*x +9393030684758*x^2 +108279046743524*x^3 + 327643477452290*x^4 +311158545054314*x^5 +92052268491098*x^6 + 6938490608252*x^7 +68699945486*x^8 +1953125*x^9)/(1-x)^10.
E.g.f.: (10077696 +118577798801*x +5170645139055*x^2 +29558124475055*x^3 +49216997902380*x^4 +32588442284937*x^5 +9880686605790*x^6 + 1438737834930*x^7 +96461496450*x^8 +2357947691*x^9)*exp(x). (End)

A017470 a(n) = (11*n + 6)^10.

Original entry on oeis.org

60466176, 2015993900449, 296196766695424, 8140406085191601, 97656250000000000, 713342911662882601, 3743906242624487424, 15516041187205853449, 53861511409489970176, 162889462677744140625

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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), this sequence (m=10), A017471 (m=11), A017472 (m=12).

List([0..20], n-> (11*n+6)^10); # G. C. Greubel, Sep 19 2019

[(11*n+6)^10: n in [0..10]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+6)^10, n=0..20); # G. C. Greubel, Sep 19 2019

(11*Range[20] -5)^10 (* G. C. Greubel, Sep 19 2019 *)

vector(20, n, (11*n-5)^10) \\ G. C. Greubel, Sep 19 2019

[(11*n+6)^10 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019:(Start)
G.f.: (60466176 +2015328772513*x +274024159430165*x^2 +4993111339147592* x^3 +24069986191404704*x^4 +38639279895450554*x^5 +21874532039020442*x^6 +4073880923146640*x^7 +193797041298488*x^8 +1099404205901*x^9 +9765625* x^10)/(1-x)^11.
E.g.f.: (60466176 +2015933434273*x +146082419680351*x^2 +1209643951056750 *x^3 +2785989264344605*x^4 +2529281956307337*x^5 +1069882300751187*x^6 + 228102792962880*x^7 +24893496850530*x^8 +1308660968505*x^9 +25937424601* x^10)*exp(x). (End)

A017471 a(n) = (11*n + 6)^11.

Original entry on oeis.org

362797056, 34271896307633, 8293509467471872, 317475837322472439, 4882812500000000000, 43513917611435838661, 269561249468963094528, 1287831418538085836267, 5062982072492057196544, 17103393581163134765625

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).

Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), this sequence (m=11), A017472 (m=12).

List([0..20], n-> (11*n+6)^11); # G. C. Greubel, Sep 19 2019

[(11*n+6)^11: n in [0..10]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+6)^11, n=0..20); # G. C. Greubel, Sep 19 2019

(11*Range[20] -5)^11 (* G. C. Greubel, Sep 19 2019 *)

vector(20, n, (11*n-5)^11) \\ G. C. Greubel, Sep 19 2019

[(11*n+6)^11 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (362797056 +34267542742961*x +7882270656385972*x^2 + 220215589053761433*x^3 +1612934439380337744*x^4 +4065965093212217778*x^5 +3893323100536505064*x^6 +1409984186533172778*x^7 +173024396961630192* x^8 +5347957556678781*x^9 +17591600106916*x^10 +48828125 x^11)/(1-x)^12.
E.g.f.: (362797056 +34271533510577*x +4112483018826831*x^2 + 48783020707697111*x^3 +152605546678854500*x^4 +184932081242538212*x^5 + 104853627173466171*x^6 +30701237124182097*x^7 +4849119426541500*x^8 + 411237867048855*x^9 +17404011907271*x^10 +285311670611*x^11)*exp(x). (End)

cp's OEIS Frontend

A017461 a(n) = 11*n + 6.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A017462 a(n) = (11*n + 6)^2.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A017463 a(n) = (11*n + 6)^3.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A017464 a(n) = (11*n + 6)^4.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A017465 a(n) = (11*n + 6)^5.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A017466 a(n) = (11*n + 6)^6.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Magma