A017506 -id:A017506 - cp's OEIS frontend

A017497 a(n) = 11*n + 9.

9, 20, 31, 42, 53, 64, 75, 86, 97, 108, 119, 130, 141, 152, 163, 174, 185, 196, 207, 218, 229, 240, 251, 262, 273, 284, 295, 306, 317, 328, 339, 350, 361, 372, 383, 394, 405, 416, 427, 438, 449, 460, 471, 482, 493, 504, 515, 526, 537, 548, 559, 570, 581, 592

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, A017413.

Powers of the form (11*n+9)^m: this sequence (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

List([0..60], n-> 11*n+9); # G. C. Greubel, Oct 28 2019

[11*n+9: n in [0..60]]; // Vincenzo Librandi, Sep 18 2011

seq(11*n+9, n=0..60); # G. C. Greubel, Oct 28 2019

Range[9, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)
(11*Range[60] - 2) (* G. C. Greubel, Oct 28 2019 *)

a(n)=11*n+9 \\ Charles R Greathouse IV, Jul 10 2016

[11*n+9 for n in (0..60)] # G. C. Greubel, Oct 28 2019

From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (9+2*x)/(1-x)^2.
E.g.f.: (9+11*x)*exp(x). (End)

A017498 a(n) = (11*n + 9)^2.

Original entry on oeis.org

81, 400, 961, 1764, 2809, 4096, 5625, 7396, 9409, 11664, 14161, 16900, 19881, 23104, 26569, 30276, 34225, 38416, 42849, 47524, 52441, 57600, 63001, 68644, 74529, 80656, 87025, 93636, 100489, 107584, 114921, 122500, 130321, 138384, 146689, 155236, 164025

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 (3,-3,1).

Powers of the form (11*n+9)^m: A017497 (m=1), this sequence (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

List([0..30], n-> (11*n+9)^2 ); # G. C. Greubel, Oct 28 2019

[(11*n+9)^2: n in [0..30]]; // G. C. Greubel, Oct 28 2019

seq((11*n+9)^2, n=0..30); # G. C. Greubel, Oct 28 2019

(11Range[0,30]+9)^2 (* or *) LinearRecurrence[{3,-3,1},{81,400,961},30] (* Harvey P. Dale, Oct 30 2011 *)

a(n)=(11*n+9)^2 \\ Charles R Greathouse IV, Jun 17 2017

[(11*n+9)^2 for n in (0..30)] # G. C. Greubel, Oct 28 2019

a(0)=81, a(1)=400, a(2)=961, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Oct 30 2011
From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (81 + 157*x +4*x^2)/(1-x)^3.
E.g.f.: (81 + 319*x + 121*x^2)*exp(x). (End)

A017499 a(n) = (11*n + 9)^3.

Original entry on oeis.org

729, 8000, 29791, 74088, 148877, 262144, 421875, 636056, 912673, 1259712, 1685159, 2197000, 2803221, 3511808, 4330747, 5268024, 6331625, 7529536, 8869743, 10360232, 12008989, 13824000, 15813251, 17984728, 20346417, 22906304, 25672375, 28652616, 31855013

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

Powers of the form (11*n+9)^m: A017497 (m=1), A017498 (m=2), this sequence (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

List([0..30], n-> (11*n+9)^3); # G. C. Greubel, Oct 28 2019

[(11*n+9)^3: n in [0..30]]; // G. C. Greubel, Oct 28 2019

seq((11*n+9)^3, n=0..30); # G. C. Greubel, Oct 28 2019

(11 Range[0,30]+9)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{729,8000,29791,74088},30] (* Harvey P. Dale, Feb 13 2018 *)

makelist( (11*n+9)^3, n, 0, 30); /* Martin Ettl, Oct 21 2012 */

vector(31, n, (11*n-2)^3) \\ G. C. Greubel, Oct 28 2019

[(11*n+9)^3 for n in (0..30)] # G. C. Greubel, Oct 28 2019

From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (729 + 5084*x + 2165*x^2 + 8*x^3)/(1-x)^4.
E.g.f.: (729 + 7271*x + 7260*x^2 + 1331*x^3)*exp(x). (End)

A017500 a(n) = (11*n + 9)^4.

Original entry on oeis.org

6561, 160000, 923521, 3111696, 7890481, 16777216, 31640625, 54700816, 88529281, 136048896, 200533921, 285610000, 395254161, 533794816, 705911761, 916636176, 1171350625, 1475789056, 1836036801, 2258530576, 2750058481, 3317760000, 3969126001, 4711998736

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+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), this sequence (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

List([0..30], n-> (11*n+9)^3); # G. C. Greubel, Oct 28 2019

[(11*n+9)^3: n in [0..30]]; // G. C. Greubel, Oct 28 2019

seq((11*n+9)^4, n=0..30); # G. C. Greubel, Oct 28 2019

(11Range[0,20]+9)^4  (* Harvey P. Dale, Mar 27 2011 *)

vector(31, n, (11*n-2)^3) \\ G. C. Greubel, Oct 28 2019

[(11*n+9)^3 for n in (0..30)] # G. C. Greubel, Oct 28 2019

From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (6561 +127195*x +189131*x^2 +28481*x^3 +16*x^4)/(1-x)^5.
E.g.f.: (6561 +153439*x +305041*x^2 +135762*x^3 +14641*x^4)*exp(x). (End)

A017501 a(n) = (11*n + 9)^5.

Original entry on oeis.org

59049, 3200000, 28629151, 130691232, 418195493, 1073741824, 2373046875, 4704270176, 8587340257, 14693280768, 23863536599, 37129300000, 55730836701, 81136812032, 115063617043, 159494694624

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+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), this sequence (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A000584.

List([0..20], n-> (11*n+9)^5); # G. C. Greubel, Oct 28 2019

[(11*n+9)^5: n in [0..20]]; // G. C. Greubel, Oct 28 2019

seq((11*n+9)^5, n=0..20); # G. C. Greubel, Oct 28 2019

(11*Range[0,20]+9)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1}, {59049,3200000,28629151,130691232,418195493,1073741824},20] (* Harvey P. Dale, Jan 25 2013 *)

vector(21, n, (11*n-2)^5) \\ G. C. Greubel, Oct 28 2019

[(11*n+9)^5 for n in (0..20)] # G. C. Greubel, Oct 28 2019

a(0)=59049, a(1)=3200000, a(2)=28629151, a(3)=130691232, a(4)=418195493, a(5)=1073741824, 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). - Harvey P. Dale, Jan 25 2013
G.f.: (59049 + 2845706*x + 10314886*x^2 + 5735346*x^3 + 371101*x^4 + 32*x^5) / (1-x)^6. - Harvey P. Dale, Jan 25 2013
E.g.f.: (59049 + 3140951*x + 11144100*x^2 + 9057455*x^3 + 2269355*x^4 + 161051*x^5)*exp(x). - G. C. Greubel, Oct 28 2019

A017502 a(n) = (11*n + 9)^6.

Original entry on oeis.org

531441, 64000000, 887503681, 5489031744, 22164361129, 68719476736, 177978515625, 404567235136, 832972004929, 1586874322944, 2839760855281, 4826809000000, 7858047974841, 12332795428864, 18755369578009

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+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), this sequence (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A001014.

List([0..20], n-> (11*n+9)^6); # G. C. Greubel, Oct 28 2019

[(11*n+9)^6: n in [0..20]]; // G. C. Greubel, Oct 28 2019

seq((11*n+9)^6, n=0..20); # G. C. Greubel, Oct 28 2019

(11Range[0,20]+9)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {531441,64000000,887503681,5489031744,22164361129,68719476736, 177978515625}, 20] (* Harvey P. Dale, Dec 06 2018 *)

makelist((11*n+9)^6, n, 0, 30); /* Martin Ettl, Oct 21 2012 */

vector(21, n, (11*n-2)^6) \\ G. C. Greubel, Oct 28 2019

[(11*n+9)^6 for n in (0..20)] # G. C. Greubel, Oct 28 2019

From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (531441 + 60279913*x + 450663942*x^2 + 601905542*x^3 + 157316657*x^4 + 4826361*x^5 + 64*x^6)/(1-x)^7.
E.g.f.: (531441 + 63468559*x + 380017561*x^2 + 502998210*x^3 + 219907820*x^4 + 35270169*x^5 + 1771561*x^6)*exp(x). (End)

A017503 a(n) = (11*n + 9)^7.

Original entry on oeis.org

4782969, 1280000000, 27512614111, 230539333248, 1174711139837, 4398046511104, 13348388671875, 34792782221696, 80798284478113, 171382426877952, 337931541778439, 627485170000000, 1107984764452581, 1874584905187328, 3057125241215467, 4828861374436224

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+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), this sequence (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A001015.

List([0..20], n-> (11*n+9)^7); # G. C. Greubel, Oct 28 2019

[(11*n+9)^7: n in [0..20]]; // G. C. Greubel, Oct 28 2019

A017503:=n->(11*n+9)^7; seq(A017503(n), n=0..50); # Wesley Ivan Hurt, Nov 20 2013

Table[(11n+9)^7, {n,0,50}] (* Wesley Ivan Hurt, Nov 20 2013 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{4782969,1280000000,27512614111,230539333248,1174711139837,4398046511104,13348388671875,34792782221696},20] (* Harvey P. Dale, Nov 12 2022 *)

vector(21, n, (11*n-2)^7) \\ G. C. Greubel, Oct 28 2019

[(11*n+9)^7 for n in (0..20)] # G. C. Greubel, Oct 28 2019

a(n) = A001015(A017497(n)). - Michel Marcus, Nov 21 2013
From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (4782969 + 1241736248*x + 17406537243*x^2 + 46010574096*x^3 + 29404476791*x^4 + 4084486872*x^5 + 62747493*x^6 + 128*x^7)/(1-x)^8.
E.g.f.: (4782969 + 1275217031*x + 12478698540*x^2 + 25306117991*x^3 + 17188094770*x^4 + 4676276836*x^5 + 520838934*x^6 + 19487171*x^7)*exp(x). (End)

A017504 a(n) = (11*n + 9)^8.

Original entry on oeis.org

43046721, 25600000000, 852891037441, 9682651996416, 62259690411361, 281474976710656, 1001129150390625, 2992179271065856, 7837433594376961, 18509302102818816, 40213853471634241, 81573072100000000

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+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), this sequence (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A001016.

List([0..20], n-> (11*n+9)^8); # G. C. Greubel, Oct 28 2019

[(11*n+9)^8: n in [0..20]]; // G. C. Greubel, Oct 28 2019

seq((11*n+9)^8, n=0..20); # G. C. Greubel, Oct 28 2019

(11*Range[0,20]+9)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1}, {43046721,25600000000,852891037441,9682651996416, 62259690411361, 281474976710656,1001129150390625, 2992179271065856, 7837433594376961}, 20] (* Harvey P. Dale, Dec 25 2013 *)

vector(21, n, (11*n-2)^8) \\ G. C. Greubel, Oct 28 2019

[(11*n+9)^8 for n in (0..20)] # G. C. Greubel, Oct 28 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, Dec 25 2013
From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (43046721 +25212579511*x +624040719397*x^2 +2924616734883*x^3 + 3674923678339*x^4 +1290563847493*x^5 +102733746903*x^6 +815728417*x^7 + 256*x^8)/(1-x)^9.
E.g.f.: (43046721 +25556953279*x +400867042081*x^2 +1200122639562*x^3 +
1189336320711*x^4 +488350759974*x^5 +90501965246*x^6 +7405124980*x^7 + 214358881*x^8)*exp(x). (End)

A017505 a(n) = (11*n + 9)^9.

Original entry on oeis.org

387420489, 512000000000, 26439622160671, 406671383849472, 3299763591802133, 18014398509481984, 75084686279296875, 257327417311663616, 760231058654565217, 1999004627104432128, 4785448563124474679

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+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), this sequence (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A001017.

List([0..20], n-> (11*n+9)^9); # G. C. Greubel, Oct 28 2019

[(11*n+9)^9: n in [0..20]]; // G. C. Greubel, Oct 28 2019

seq((11*n+9)^9, n=0..20); # G. C. Greubel, Oct 28 2019

(11*Range[20] -2)^9 (* G. C. Greubel, Oct 28 2019 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{387420489,512000000000,26439622160671,406671383849472,3299763591802133,18014398509481984,75084686279296875,257327417311663616,760231058654565217,1999004627104432128},20] (* Harvey P. Dale, Nov 18 2022 *)

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

vector(21, n, (11*n-2)^9) \\ G. C. Greubel, Oct 28 2019

[(11*n+9)^9 for n in (0..20)] # G. C. Greubel, Oct 28 2019

From G. C. Greubel, Oct 28 2019: (Start)
G.f.: (387420489 + 508125795110*x + 21337056082676*x^2 + 165268671784082*x^3 + 361474108840298*x^4 + 251642575443146*x^5 + 52874765679980*x^6 + 2535762569534*x^7 + 10604494253*x^8 + 512*x^9)/(1-x)^10.
E.g.f.: (387420489 + 511612579511*x + 12708004790580*x^2 + 54814688324495* x^3 + 76236174032865*x^4 + 44337148166157*x^5 + 12159505753164*x^6 + 1632362365986*x^7 + 102249186237*x^8 + 2357947691*x^9)*exp(x). (End)

A017508 a(n) = (11*n + 9)^12.

Original entry on oeis.org

282429536481, 4096000000000000, 787662783788549761, 30129469486639681536, 491258904256726154641, 4722366482869645213696, 31676352024078369140625, 163674647745587512938496, 693842360995438000295041, 2518170116818978404827136

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 (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

Powers of the form (11*n+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), this sequence (m=12).

List([0..20], n-> (11*n+9)^12); # G. C. Greubel, Oct 29 2019

[(11*n+9)^12: n in [0..20]]; // G. C. Greubel, Oct 29 2019

seq((11*n+9)^12, n=0..0); # G. C. Greubel, Oct 28 2019

(11*Range[20] -2)^12 (* G. C. Greubel, Oct 29 2019 *)

makelist((11*n+9)^12, n,0,30); /* Martin Ettl, Oct 21 2012 */

vector(21, n, (11*n-2)^12) \\ G. C. Greubel, Oct 29 2019

[(11*n+9)^12 for n in (0..20)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (282429536481 +4092328416025747*x +734436813292395279*x^2 + 20209260522541101077*x^3 +159842244003035759946*x^4 + 463756067839761680478*x^5 +544661828676570185790*x^6 +
262487410539784705770*x^7 +48674358916489218693*x^8 + 2906273242026287199*x^9 +36217472329783811*x^10 +23298085069233*x^11 + 4096*x^12)/(1-x)^13.
E.g.f.: (282429536481 + 4095717570463519*x + 389735533109043121*x^2 + 4629794808807415962*x^3 +15643775803972010981*x^4 +21329254236100801848* x^5 +14055885648635908792*x^6 +4951158185239377540*x^7 + 983467446953859582*x^8 +112116203770421565*x^9 +7184433177655591*x^10 + 237949933289574*x^11 +3138428376721*x^12)*exp(x). (End)

cp's OEIS Frontend

A017497 a(n) = 11*n + 9.

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A017498 a(n) = (11*n + 9)^2.

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A017499 a(n) = (11*n + 9)^3.

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A017500 a(n) = (11*n + 9)^4.

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A017501 a(n) = (11*n + 9)^5.

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A017502 a(n) = (11*n + 9)^6.

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