A017478 -id:A017478 - cp's OEIS frontend

A017473 a(n) = 11*n + 7.

7, 18, 29, 40, 51, 62, 73, 84, 95, 106, 117, 128, 139, 150, 161, 172, 183, 194, 205, 216, 227, 238, 249, 260, 271, 282, 293, 304, 315, 326, 337, 348, 359, 370, 381, 392, 403, 414, 425, 436, 447, 458, 469, 480, 491, 502, 513, 524, 535, 546, 557, 568, 579, 590

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+7)^m: this sequence (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

List([0..60], n-> 11*n+7); # G. C. Greubel, Sep 19 2019

[(11*n+7): n in [0..60]]; // Vincenzo Librandi, Sep 04 2011

seq(11*n+7, n=0..60); # G. C. Greubel, Sep 19 2019

Range[7, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)

vector(60, n, 11*n-4) \\ G. C. Greubel, Sep 19 2019

[11*n+7 for n in (0..60)] # G. C. Greubel, Sep 19 2019

From Colin Barker, Jun 06 2012: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (7 + 4*x)/(1-x)^2. (End)
E.g.f.: (7 + 11*x)*exp(x). - G. C. Greubel, Sep 19 2019

A017474 a(n) = (11*n + 7)^2.

Original entry on oeis.org

49, 324, 841, 1600, 2601, 3844, 5329, 7056, 9025, 11236, 13689, 16384, 19321, 22500, 25921, 29584, 33489, 37636, 42025, 46656, 51529, 56644, 62001, 67600, 73441, 79524, 85849, 92416, 99225, 106276, 113569, 121104, 128881, 136900, 145161, 153664, 162409, 171396, 180625, 190096, 199809

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+7)^m: A017473 (m=1), this sequence (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

List([0..50], n-> (11*n+7)^2); # G. C. Greubel, Sep 19 2019

[(11*n+7)^2: n in [0..50]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+7)^2, n=0..50); # G. C. Greubel, Sep 19 2019

(11 Range[0,50]+7)^2 (* or *) LinearRecurrence[{3,-3,1},{49,324,841},50] (* Harvey P. Dale, May 19 2019 *)

a(n)=(11*n+7)^2 \\ Charles R Greathouse IV, Jun 17 2017

[(11*n+7)^2 for n in (0..50)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (49 +177*x +16*x^2)/(1-x)^3.
E.g.f.: (49 +275*x +121*x^2)*exp(x). (End)

A017475 a(n) = (11*n + 7)^3.

Original entry on oeis.org

343, 5832, 24389, 64000, 132651, 238328, 389017, 592704, 857375, 1191016, 1601613, 2097152, 2685619, 3375000, 4173281, 5088448, 6128487, 7301384, 8615125, 10077696, 11697083, 13481272, 15438249, 17576000, 19902511, 22425768, 25153757, 28094464, 31255875, 34645976, 38272753, 42144192

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+7)^m: A017473 (m=1), A017474 (m=2), this sequence (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

List([0..40], n-> (11*n+7)^3); # G. C. Greubel, Sep 19 2019

[(11*n+7)^3: n in [0..40]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+7)^3, n=0..40); # G. C. Greubel, Sep 19 2019

(11*Range[0,40]+7)^3 (* or *) LinearRecurrence[{4,-6,4,-1},{343,5832, 24389,64000}, 40] (* Harvey P. Dale, Oct 18 2014 *)

makelist((11*n+7)^3, n,0,40); /* Martin Ettl, Oct 21 2012 */

a(n) = (11*n+7)^3; \\ Altug Alkan, Sep 08 2018

[(11*n+7)^3 for n in (0..40)] # G. C. Greubel, Sep 19 2019

G.f.: (343 + 4460*x + 3119*x^2 + 64*x^3)/(1-x)^4. - R. J. Mathar, Jun 24 2009
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=343, a(1)=5832, a(2)=24389, a(3)=64000. - Harvey P. Dale, Oct 18 2014
E.g.f.: (343 +5489*x +6534*x^2 +1331*x^3)*exp(x). - G. C. Greubel, Sep 19 2019

A017476 a(n) = (11*n + 7)^4.

Original entry on oeis.org

2401, 104976, 707281, 2560000, 6765201, 14776336, 28398241, 49787136, 81450625, 126247696, 187388721, 268435456, 373301041, 506250000, 671898241, 875213056, 1121513121, 1416468496, 1766100625, 2176782336, 2655237841, 3208542736, 3844124001, 4569760000

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+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), this sequence (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

List([0..30], n-> (11*n+7)^4); # G. C. Greubel, Sep 19 2019

[(11*n+7)^4: n in [0..30]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+7)^4, n=0..30); # G. C. Greubel, Sep 19 2019

(11*Range[0,30]+7)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1}, {2401, 104976,707281,2560000,6765201}, 30] (* Harvey P. Dale, Oct 21 2015 *)

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

[(11*n+7)^4 for n in (0..30)] # G. C. Greubel, Sep 19 2019

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=2401, a(1)=104976, a(2)=707281, a(3)=2560000, a(4)=6765201. - Harvey P. Dale, Oct 21 2015
From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (2401 +92971*x +206411*x^2 +49345*x^3 +256*x^4)/(1-x)^5.
E.g.f.: (2401 +102575*x +249865*x^2 +125114*x^3 +14641 x^4)*exp(x). (End)

A017477 a(n) = (11*n + 7)^5.

Original entry on oeis.org

16807, 1889568, 20511149, 102400000, 345025251, 916132832, 2073071593, 4182119424, 7737809375, 13382255776, 21924480357, 34359738368, 51888844699, 75937500000, 108175616801, 150536645632, 205236901143

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+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), this sequence (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

List([0..30], n-> (11*n+7)^5); # G. C. Greubel, Sep 19 2019

[(11*n+7)^5: n in [0..30]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+7)^5, n=0..30); # G. C. Greubel, Sep 19 2019

(11 * Range[0, 30] + 7)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1}, {16807, 1889568, 20511149, 102400000, 345025251, 916132832}, 30] (* Harvey P. Dale, Jan 16 2013 *)

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

[(11*n+7)^5 for n in (0..30)] # G. C. Greubel, Sep 19 2019

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), with a(0) = 16807, a(1) = 1889568, a(2) = 20511149, a(3) = 102400000, a(4) = 345025251, a(5) = 916132832. - Harvey P. Dale, Jan 16 2013
From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (16807 +1788726*x +9425846*x^2 +7340486*x^3 +753231*x^4 +1024*x^5 )/(1-x)^6.
E.g.f.: (16807 +1872761*x +8374410*x^2 +7753075*x^3 +2122945*x^4 +161051 *x^5)*exp(x). (End)

A017479 a(n) = (11*n + 7)^7.

Original entry on oeis.org

823543, 612220032, 17249876309, 163840000000, 897410677851, 3521614606208, 11047398519097, 29509034655744, 69833729609375, 150363025899136, 300124211606973, 562949953421312, 1002544368429379, 1708593750000000, 2804020163098721, 4453476124377088, 6873178582377927

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+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), this sequence (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

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

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

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

(11Range[0,20]+7)^7  (* Harvey P. Dale, Mar 24 2011 *)

vector(20, n, (11*n-4)^7) \\ G. C. Greubel, Sep 19 2019

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

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (823543 +605631688*x +12375175257*x^2 +42937032016*x^3 +35460540721 *x^4 +6665393928*x^5 +170728303*x^6 +16384*x^7)/(1-x)^8.
E.g.f.: (823543 +611396489*x +8013129894*x^2 +18987701271*x^3 + 14295911630*x^4 +4196022754*x^5 +496037080*x^6 +19487171*x^7)*exp(x). (End)

A017480 a(n) = (11*n + 7)^8.

Original entry on oeis.org

5764801, 11019960576, 500246412961, 6553600000000, 45767944570401, 218340105584896, 806460091894081, 2478758911082496, 6634204312890625, 15938480745308416, 35114532758015841, 72057594037927936, 139353667211683681, 256289062500000000, 451447246258894081

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 (9,-36,84,-126,126,-84,36,-9,1).

Powers of the form (11*n+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), this sequence (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

List([0..20], n-> (11*n+7)^8); # G. C. Greubel, Sep 19 2019

[(11*n+7)^8: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+7)^8, n=0..20); # G. C. Greubel, Sep 19 2019

(11*Range[0,20]+7)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36, -9,1}, {5764801,11019960576, 500246412961,6553600000000, 45767944570401, 218340105584896,806460091894081,2478758911082496,6634204312890625}, 20] (* Harvey P. Dale, Mar 30 2016 *)

vector(20, n, (11*n-4)^8) \\ G. C. Greubel, Sep 19 2019

[(11*n+7)^8 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (5764801 +10968077367*x +401274300613*x^2 +2447616620803*x^3 + 3869465113539*x^4 +1725294430213*x^5 +185763408247*x^6 +2562300801*x^7 + 65536*x^8)/(1-x)^9.
E.g.f.: (5764801 +11014195775*x +239106128305*x^2 +847652479674*x^3 + 937956207111*x^4 +417408438678*x^5 +82366957134*x^6 +7093330244*x^7 + 214358881*x^8)*exp(x). (End)

A017481 a(n) = (11*n + 7)^9.

Original entry on oeis.org

40353607, 198359290368, 14507145975869, 262144000000000, 2334165173090451, 13537086546263552, 58871586708267913, 208215748530929664, 630249409724609375, 1689478959002692096, 4108400332687853397, 9223372036854775808, 19370159742424031659, 38443359375000000000

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+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), this sequence (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

List([0..20], n-> (11*n+7)^9); # G. C. Greubel, Sep 19 2019

[(11*n+7)^9: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+7)^9, n=0..20); # G. C. Greubel, Sep 19 2019

(11Range[0,20]+7)^9  (* Harvey P. Dale, Mar 23 2011 *)

makelist((11*n+7)^9, n, 0, 30); /* Martin Ettl, Oct 21 2012 */

a(n) = (11*n+7)^9; \\ Altug Alkan, Sep 08 2018

[(11*n+7)^9 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (40353607 +197955754298*x +12525368984504*x^2 +125993865875030*x^3 +341752101417866*x^4 +292702580123078*x^5 +77396622719912*x^6 + 5045081881706*x^7 +38440737935*x^8 +262144*x^9)/(1-x)^10.
E.g.f.: (40353607 +198318936761*x +7055233874370*x^2 +36536266598315*x^3 +57159943839075*x^4 +36196841476257*x^5 +10604280696240*x^6 + 1501876268970*x^7 +98390726379*x^8 +2357947691*x^9)*exp(x). (End)

A017482 a(n) = (11*n + 7)^10.

Original entry on oeis.org

282475249, 3570467226624, 420707233300201, 10485760000000000, 119042423827613001, 839299365868340224, 4297625829703557649, 17490122876598091776, 59873693923837890625, 179084769654285362176, 480682838924478847449, 1180591620717411303424, 2692452204196940400601

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+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), A017481 (m=9), this sequence (m=10), A017483 (m=11), A017484 (m=12).

List([0..20], n-> (11*n+7)^10); # G. C. Greubel, Sep 19 2019

[(11*n+7)^10: n in [0..10]]; // Vincenzo Librandi, Sep 04 2011

seq((11*n+7)^10, n=0..20); # G. C. Greubel, Sep 19 2019

(11*Range[21] -4)^10 (* G. C. Greubel, Sep 19 2019 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{282475249,3570467226624,420707233300201,10485760000000000,119042423827613001,839299365868340224,4297625829703557649,17490122876598091776,59873693923837890625,179084769654285362176,480682838924478847449},30] (* Harvey P. Dale, Apr 21 2020 *)

vector(20, n, (11*n-4)^10) \\ G. C. Greubel, Sep 19 2019

[(11*n+7)^10 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (282475249 +3567359998885*x +381447629946032*x^2 +6054309522746024* x^3 +26248927783563266*x^4 +38310933951284930*x^5 +19699677304461320*x^6 +3287461918700048*x^7 +134823999028181*x^8 +576638856289*x^9 +1048576* x^10)/(1-x)^11.
E.g.f.: (282475249 +3570184751375*x +206783290661101*x^2 + 1539058236550670*x^3 +3317056068374290*x^4 +2872963553757759*x^5 +1172277747064347*x^6 +242804694252120 x^7 +25867757964675*x^8 +1332240445415*x^9 +25937424601*x^10)*exp(x). (End)

A017483 a(n) = (11*n + 7)^11.

Original entry on oeis.org

1977326743, 64268410079232, 12200509765705829, 419430400000000000, 6071163615208263051, 52036560683837093888, 313726685568359708377, 1469170321634239709184, 5688000922764599609375, 18982985583354248390656, 56239892154164025151533, 151115727451828646838272

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+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), this sequence (m=11), A017484 (m=12).

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

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

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

(11*Range[21] -4)^11 (* G. C. Greubel, Sep 19 2019 *)

vector(20, n, (11*n-4)^11) \\ G. C. Greubel, Sep 19 2019

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

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (1977326743 +64244682158316*x +11429419348320083*x^2 + 277265562864875904*x^3 +1829094388304154510*x^4 +4212702849829094280*x^5 +3698421546351487230*x^6 +1221731311784947392*x^7 +134444370899578971* x^8 +3566547693499340*x^9 +8649705527727*x^10 +4194304*x^11)/(1-x)^12.
E.g.f.: (1977326743 +64266432752489*x +6035987461437054*x^2 + 63836945659298911*x^3 +186099500089146160*x^4 +214611357085098248*x^5 + 117178874627032680*x^6 +33290649534885897*x^7 +5128288643417445*x^8 + 425762824825415*x^9 +17689323577882*x^10 +285311670611*x^11)*exp(x). (End)

cp's OEIS Frontend

A017473 a(n) = 11*n + 7.

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A017474 a(n) = (11*n + 7)^2.

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A017475 a(n) = (11*n + 7)^3.

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A017476 a(n) = (11*n + 7)^4.

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A017477 a(n) = (11*n + 7)^5.

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A017479 a(n) = (11*n + 7)^7.

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