A017488 -id:A017488 - cp's OEIS frontend

A017485 a(n) = 11*n + 8.

8, 19, 30, 41, 52, 63, 74, 85, 96, 107, 118, 129, 140, 151, 162, 173, 184, 195, 206, 217, 228, 239, 250, 261, 272, 283, 294, 305, 316, 327, 338, 349, 360, 371, 382, 393, 404, 415, 426, 437, 448, 459, 470, 481, 492, 503, 514, 525, 536, 547, 558, 569, 580, 591, 602, 613

Offset: 0

N. J. A. Sloane, Dec 11 1996

a(n) = A125199(n+1,3) for n>1. - Reinhard Zumkeller, Nov 24 2006

G. C. Greubel, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A002939, A016789, A017041, A125202.

Powers of the form (11*n+8)^m: this sequence (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

List([0..60], n-> 11*n+8); # G. C. Greubel, Sep 21 2019

[11*n+8 : n in [0..60]]; // Wesley Ivan Hurt, May 21 2014

A017485:=n->11*n+8; seq(A017485(n), n=0..60); # Wesley Ivan Hurt, May 21 2014

Range[8, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)
LinearRecurrence[{2,-1},{8,19},60] (* Harvey P. Dale, May 10 2021 *)

Vec((8+3*x)/(1-x)^2 + O(x^60)) \\ Colin Barker, Oct 05 2014

[11*n+8 for n in (0..60)] # G. C. Greubel, Sep 22 2019

a(n) = 22*n + 5 - a(n-1), with n>0, a(0)=8. - Vincenzo Librandi, Dec 24 2010
From Colin Barker, Oct 05 2014: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (8 + 3*x)/(1-x)^2. (End)
E.g.f.: (8 + 11*x)*exp(x). - G. C. Greubel, Sep 21 2019

A017486 a(n) = (11*n + 8)^2.

Original entry on oeis.org

64, 361, 900, 1681, 2704, 3969, 5476, 7225, 9216, 11449, 13924, 16641, 19600, 22801, 26244, 29929, 33856, 38025, 42436, 47089, 51984, 57121, 62500, 68121, 73984, 80089, 86436, 93025, 99856, 106929, 114244, 121801, 129600, 137641, 145924, 154449, 163216, 172225, 181476, 190969, 200704

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+8)^m: A017485 (m=1), this sequence (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

List([0..45], n-> (11*n+8)^2); # G. C. Greubel, Sep 21 2019

[(11*n+8)^2: n in [0..45]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+8)^2, n=0..45); # G. C. Greubel, Sep 21 2019

(11*Range[45]-3)^2 (* G. C. Greubel, Sep 21 2019 *)

a(n)=(11*n+8)^2 \\ Charles R Greathouse IV, Jun 17 2017

[(11*n+8)^2 for n in (0..45)] # G. C. Greubel, Sep 21 2019

From G. C. Greubel, Sep 21 2019: (Start)
G.f.: (64 + 169*x + 9*x^2)/(1-x)^3.
E.g.f.: (64 + 297*x + 121*x^2)*exp(x). (End)

A017487 a(n) = (11*n + 8)^3.

Original entry on oeis.org

512, 6859, 27000, 68921, 140608, 250047, 405224, 614125, 884736, 1225043, 1643032, 2146689, 2744000, 3442951, 4251528, 5177717, 6229504, 7414875, 8741816, 10218313, 11852352, 13651919, 15625000, 17779581, 20123648, 22665187, 25412184, 28372625, 31554496, 34965783, 38614472, 42508549

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+8)^m: A017485 (m=1), A017486 (m=2), this sequence (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

List([0..40], n-> (11*n+8)^3); # G. C. Greubel, Sep 21 2019

[(11*n+8)^3: n in [0..40]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+8)^3, n=0..40); # G. C. Greubel, Sep 21 2019

(11*Range[50] - 3)^3 (* G. C. Greubel, Sep 21 2019 *)

makelist( (11*n+8)^3, n, 0, 30); /* Martin Ettl, Oct 21 2012 */

a(n) = (11*n+8)^3; \\ Altug Alkan, Sep 08 2018

[(11*n+8)^3 for n in (0..40)] # G. C. Greubel, Sep 21 2019

From G. C. Greubel, Sep 21 2019: (Start)
G.f.: (512 + 4811*x + 2636*x^2 + 27*x^3)/(1-x)^4.
E.g.f.: (512 + 6347*x + 6897*x^2 + 1331*x^3)*exp(x). (End)

A017489 a(n) = (11*n + 8)^5.

Original entry on oeis.org

32768, 2476099, 24300000, 115856201, 380204032, 992436543, 2219006624, 4437053125, 8153726976, 14025517307, 22877577568, 35723051649, 53782400000, 78502725751, 111577100832, 154963892093, 210906087424, 281950621875, 370967703776, 481170140857, 616132666368

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+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), this sequence (m=5), A017490 (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

List([0..30], n-> (11*n+8)^5); # G. C. Greubel, Sep 22 2019

[(11*n+8)^5: n in [0..30]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+8)^5, n=0..30); # G. C. Greubel, Sep 22 2019

(11*Range[31] -3)^5 (* G. C. Greubel, Sep 22 2019 *)

vector(30, n, (11*n-3)^5) \\ G. C. Greubel, Sep 22 2019

[(11*n+8)^5 for n in (0..30)] # G. C. Greubel, Sep 22 2019

From G. C. Greubel, Sep 22 2019: (Start)
G.f.: (32768 +2279491*x +9934926*x^2 +6542326*x^3 +536366*x^4 +243*x^5 )/(1-x)^6.
E.g.f.: (32768 +2443331*x +9690285*x^2 +8391955*x^3 +2196150*x^4 +161051* x^5)*exp(x). (End)

A017490 a(n) = (11*n + 8)^6.

Original entry on oeis.org

262144, 47045881, 729000000, 4750104241, 19770609664, 62523502209, 164206490176, 377149515625, 782757789696, 1500730351849, 2699554153024, 4608273662721, 7529536000000, 11853911588401, 18075490334784, 26808753332089, 38806720086016, 54980371265625

Offset: 0

N. J. A. Sloane, Dec 11 1996

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+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), this sequence (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

List([0..20], n-> (11*n+8)^6); # G. C. Greubel, Sep 22 2019

[(11*n+8)^6: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011

A017490:=n->(11*n+8)^6; seq(A017490(n), n=0..20); # Wesley Ivan Hurt, May 21 2014

(11*Range[0,20]+8)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {262144, 47045881, 729000000, 4750104241, 19770609664, 62523502209, 164206490176}, 20] (* Harvey P. Dale, Nov 08 2013 *)

makelist( (11*n+8)^6, n, 0, 20); /* Martin Ettl, Oct 21 2012 */

vector(20, n, (11*n-3)^6) \\ G. C. Greubel, Sep 22 2019

[(11*n+8)^6 for n in (0..20)] # G. C. Greubel, Sep 22 2019

a(0)=262144, a(1)=47045881, a(2)=729000000, a(3)=4750104241, a(4)=19770609664, a(5)=62523502209, a(6)=164206490176, 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, Nov 08 2013
a(n) = A001014(A017485(n)). - Wesley Ivan Hurt, May 21 2014
From G. C. Greubel, Sep 22 2019: (Start)
G.f.: (262144 +45210873*x +405183857*x^2 +625892702*x^3 +191449182*x^4 +7524433*x^5 +729*x^6)/(1-x)^7.
E.g.f.: (262144 +46783737*x +317585191*x^2 +450663290*x^3 +206511305*x^4 + 34303863*x^5 +1771561*x^6)*exp(x). (End)

A017491 a(n) = (11*n + 8)^7.

Original entry on oeis.org

2097152, 893871739, 21870000000, 194754273881, 1028071702528, 3938980639167, 12151280273024, 32057708828125, 75144747810816, 160578147647843, 318547390056832, 594467302491009, 1054135040000000, 1789940649848551, 2928229434235008, 4637914326451397, 7140436495826944

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+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), this sequence (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

List([0..20], n-> (11*n+8)^7); # G. C. Greubel, Sep 22 2019

[(11*n+8)^7: n in [0..20]]; // G. C. Greubel, Sep 22 2019

seq((11*n+8)^7, n=0..20); # G. C. Greubel, Sep 22 2019

(11*Range[0,20]+8)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8, -1}, {2097152, 893871739, 21870000000, 194754273881, 1028071702528, 3938980639167, 12151280273024, 32057708828125}, 20] (* Harvey P. Dale, Aug 14 2015 *)

vector(20, n, (11*n-3)^7) \\ G. C. Greubel, Sep 22 2019

[(11*n+8)^7 for n in (0..20)] # G. C. Greubel, Sep 22 2019

G.f.: (2097152 +877094523*x +14777746344*x^2 +44705242061*x^3 +32487494736*x^4 +5260268829*x^5 +105396008*x^6 +2187*x^7)/(1-x)^8. - R. J. Mathar, Jun 24 2009
a(0)=2097152, a(1)=893871739, a(2)=21870000000, a(3)=194754273881, a(4)=1028071702528, a(5)=3938980639167, a(6)=12151280273024, a(7)=32057708828125, 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, Aug 14 2015
E.g.f.: (2097152 +891774587*x +10042176837*x^2 +21970631991*x^3 + 15695884050*x^4 +4432767724*x^5 +508438007*x^6 +19487171*x^7)*exp(x). - G. C. Greubel, Sep 22 2019

More terms added by G. C. Greubel, Sep 22 2019

A017492 a(n) = (11*n + 8)^8.

Original entry on oeis.org

16777216, 16983563041, 656100000000, 7984925229121, 53459728531456, 248155780267521, 899194740203776, 2724905250390625, 7213895789838336, 17181861798319201, 37588592026706176, 76686282021340161, 147578905600000000, 270281038127131201, 474373168346071296

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+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), this sequence (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

List([0..20], n-> (11*n+8)^8); # G. C. Greubel, Sep 22 2019

[(11*n+8)^8: n in [0..20]]; // G. C. Greubel, Sep 22 2019

seq((11*n+8)^8, n=0..20); # G. C. Greubel, Sep 22 2019

(11*Range[21] -3)^8 (* G. C. Greubel, Sep 22 2019 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{16777216,16983563041,656100000000,7984925229121,53459728531456,248155780267521,899194740203776,2724905250390625,7213895789838336},20] (* Harvey P. Dale, Jul 02 2024 *)

vector(20, n, (11*n-3)^8) \\ G. C. Greubel, Sep 22 2019

[(11*n+8)^8 for n in (0..20)] # G. C. Greubel, Sep 22 2019

From G. C. Greubel, Sep 22 2019: (Start)
G.f.: (16777216 +16832568097*x +503851912407*x^2 +2690024212453*x^3 + 3790496103139*x^4 +1500946746723*x^5 +139306025317*x^6 +1475730007*x^7 + 6561*x^8)/(1-x)^9.
E.g.f.: (16777216 +16966785825*x +311074825567*x^2 +1011259856838*x^3 + 1057862922501*x^4 +451919091162*x^5 +86384857482*x^6 +7249227612*x^7 + 214358881*x^8)*exp(x). (End)

More terms added by G. C. Greubel, Sep 22 2019

A017493 a(n) = (11*n + 8)^9.

Original entry on oeis.org

134217728, 322687697779, 19683000000000, 327381934393961, 2779905883635712, 15633814156853823, 66540410775079424, 231616946283203125, 692533995824480256, 1838459212420154507, 4435453859151328768, 9892530380752880769, 20661046784000000000, 40812436757196811351

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+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), A017492 (m=8), this sequence (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

List([0..20], n-> (11*n+8)^9); # G. C. Greubel, Sep 22 2019

[(11*n+8)^9: n in [0..20]]; // G. C. Greubel, Sep 22 2019

seq((11*n+8)^9, n=0..20); # G. C. Greubel, Sep 22 2019

(11Range[0,10]+8)^9  (* Harvey P. Dale, Apr 06 2011 *)

makelist( (11*n+8)^9, n, 0, 30); /* Martin Ettl, Oct 21 2012 */

vector(20, n, (11*n-3)^9) \\ G. C. Greubel, Sep 22 2019

[(11*n+8)^9 for n in (0..20)] # G. C. Greubel, Sep 22 2019

From G. C. Greubel, Sep 22 2019: (Start)
G.f.: (134217728 +321345520499*x +16462162819970*x^2 +145056774666656*x^3 +353127201685502*x^4 +272712961891082*x^5 +64342728755486*x^6 + 3608087683520*x^7 +20660849954*x^8 +19683*x^9)/(1-x)^10.
E.g.f.: (134217728 +322553480051*x +9518879411085*x^2 +44883477211595*x^3 +66132730395270*x^4 +40107394890717*x^5 +11363589456450*x^6 + 1566417779322*x^7 +100319956308*x^8 +2357947691*x^9)*exp(x). (End)

More terms added by G. C. Greubel, Sep 22 2019

A017494 a(n) = (11*n + 8)^10.

Original entry on oeis.org

1073741824, 6131066257801, 590490000000000, 13422659310152401, 144555105949057024, 984930291881790849, 4923990397355877376, 19687440434072265625, 66483263599150104576, 196715135728956532249, 523383555379856794624, 1276136419117121619201, 2892546549760000000000

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+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), this sequence (m=10), A017495 (m=11), A017496 (m=12).

List([0..20], n-> (11*n+8)^10); # G. C. Greubel, Sep 22 2019

[(11*n+8)^10: n in [0..20]]; // G. C. Greubel, Sep 22 2019

seq((11*n+8)^10, n=0..20); # G. C. Greubel, Sep 22 2019

(11*Range[21] -3)^10 (* G. C. Greubel, Sep 22 2019 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1073741824,6131066257801,590490000000000,13422659310152401,144555105949057024,984930291881790849,4923990397355877376,19687440434072265625,66483263599150104576,196715135728956532249,523383555379856794624},20] (* Harvey P. Dale, May 08 2022 *)

vector(20, n, (11*n-3)^10) \\ G. C. Greubel, Sep 22 2019

[(11*n+8)^10 for n in (0..20)] # G. C. Greubel, Sep 22 2019

From G. C. Greubel, Sep 22 2019: (Start)
G.f.: (1073741824 +6119255097737*x +523107326964509*x^2 +7264300786930496 *x^3 +28371531939645368*x^4 +37662294296897282*x^5 +17578871136786818* x^6 +2623025688296696*x^7 +92185633683584*x^8 +289254005437*x^9 +59049* x^10)/(1-x)^11.
E.g.f.: (1073741824 +6129992515977*x +289114470613111*x^2 +1944930239197330*x^3 +3932620229881585*x^4 +3254225912463141*x^5 + 1282086963575187*x^6 +258144995263320*x^7 +26861311378110*x^8 + 1355819922325*x^9 +25937424601*x^10)*exp(x). (End)

More terms added by G. C. Greubel, Sep 22 2019

A017495 a(n) = (11*n + 8)^11.

Original entry on oeis.org

8589934592, 116490258898219, 17714700000000000, 550329031716248441, 7516865509350965248, 62050608388552823487, 364375289404334925824, 1673432436896142578125, 6382393305518410039296, 21048519522998348950643, 61759259534823101765632, 164621598066108688876929

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+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), this sequence (m=11), A017496 (m=12).

List([0..20], n-> (11*n+8)^11); # G. C. Greubel, Sep 22 2019

[(11*n+8)^11: n in [0..20]]; // G. C. Greubel, Sep 22 2019

seq((11*n+8)^11, n=0..20); # G. C. Greubel, Sep 22 2019

(11*Range[0,20]+8)^11 (* Harvey P. Dale, Dec 18 2011 *)

vector(20, n, (11*n-3)^11) \\ G. C. Greubel, Sep 22 2019

[(11*n+8)^11 for n in (0..20)] # G. C. Greubel, Sep 22 2019

From G. C. Greubel, Sep 22 2019: (Start)
G.f.: (8589934592 +116387179683115*x +16317383828904444*x^2 + 345439099017920655*x^3 +2056463723815998816*x^4 +4330360244540059158*x^5 +3485249533342266888*x^6 +1049164126934199606*x^7 +103278745612305120* x^8 +2335591020671359*x^9 +4049563043900*x^10 +177147*x^11)/(1-x)^12.
E.g.f.: (8589934592 +116481668963627*x +8740864036069077*x^2 + 82922398983834751*x^3 +225890484585013050*x^4 +248275055013875318*x^5 + 130670920341658389*x^6 +36045281196709257*x^7 +5418280840195080*x^8 + 440547156847985*x^9 +17974635248493*x^10 +285311670611*x^11)*exp(x). (End)

More terms added by G. C. Greubel, Sep 22 2019

cp's OEIS Frontend

A017485 a(n) = 11*n + 8.

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A017486 a(n) = (11*n + 8)^2.

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A017487 a(n) = (11*n + 8)^3.

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A017489 a(n) = (11*n + 8)^5.

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A017490 a(n) = (11*n + 8)^6.

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A017491 a(n) = (11*n + 8)^7.

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