A017438 -id:A017438 - cp's OEIS frontend

A017437 a(n) = 11*n + 4.

4, 15, 26, 37, 48, 59, 70, 81, 92, 103, 114, 125, 136, 147, 158, 169, 180, 191, 202, 213, 224, 235, 246, 257, 268, 279, 290, 301, 312, 323, 334, 345, 356, 367, 378, 389, 400, 411, 422, 433, 444, 455, 466, 477, 488, 499, 510, 521, 532, 543, 554, 565, 576, 587

Offset: 0

N. J. A. Sloane

These numbers do not occur in A000045 (Fibonacci numbers). - Arkadiusz Wesolowski, Jan 08 2012

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, A017425.

Powers of the form (11*n+4)^m: this sequence (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

List([0..60], n-> 11*n+4); # G. C. Greubel, Sep 18 2019

[11*n+4: n in [0..60]]; // Vincenzo Librandi, Sep 18 2011

seq(11*n+4, n=0..60); # G. C. Greubel, Sep 18 2019

Range[4, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
LinearRecurrence[{2,-1},{4,15},60] (* Harvey P. Dale, May 19 2012 *)

a(n)=11*n+4 \\ Charles R Greathouse IV, Oct 07 2015

list(range(4, 600, 11))  # Zerinvary Lajos, May 21 2009

a(0)=4, a(1)=15, a(n) = 2*a(n-1) - a(n-2). - Harvey P. Dale, May 19 2012
From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (4 + 7*x)/(1-x)^2.
E.g.f.: (4 + 11*x)*exp(x). (End)

A017439 a(n) = (11*n + 4)^3.

Original entry on oeis.org

64, 3375, 17576, 50653, 110592, 205379, 343000, 531441, 778688, 1092727, 1481544, 1953125, 2515456, 3176523, 3944312, 4826809, 5832000, 6967871, 8242408, 9663597, 11239424, 12977875, 14886936, 16974593, 19248832, 21717639, 24389000, 27270901, 30371328, 33698267, 37259704, 41063625

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+4)^m: A017437 (m=1), A017438 (m=2), this sequence (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

List([0..40], n-> (11*n + 4)^3); # G. C. Greubel, Sep 18 2019

[(11*n + 4)^3: n in [0..40]]; // G. C. Greubel, Sep 18 2019

seq((11*n + 4)^3, n=0..40); # G. C. Greubel, Sep 18 2019

(11*Range[40] -7)^3 (* G. C. Greubel, Sep 18 2019 *)
LinearRecurrence[{4,-6,4,-1},{64,3375,17576,50653},40] (* Harvey P. Dale, Feb 10 2024 *)

vector(40, n, (11*n-7)^3) \\ G. C. Greubel, Sep 18 2019

[(11*n + 4)^3 for n in (0..40)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (64 + 3119*x + 4460*x^2 + 343*x^3)/(1-x)^4.
E.g.f.: (64 + 3311*x + 5445*x^2 + 1331*x^3)*exp(x). (End)

Terms a(23) onward added by G. C. Greubel, Sep 18 2019

A017440 a(n) = (11*n + 4)^4.

Original entry on oeis.org

256, 50625, 456976, 1874161, 5308416, 12117361, 24010000, 43046721, 71639296, 112550881, 168896016, 244140625, 342102016, 466948881, 623201296, 815730721, 1049760000, 1330863361, 1664966416, 2058346161, 2517630976, 3049800625, 3662186256, 4362470401, 5158686976, 6059221281

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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), this sequence (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

List([0..30], n-> (11*n+4)^4); # G. C. Greubel, Sep 18 2019

[(11*n+4)^4: n in [0..30]]; // G. C. Greubel, Sep 18 2019

seq((11*n + 4)^4, n=0..30); # G. C. Greubel, Sep 18 2019

(11*Range[30] -7)^4 (* G. C. Greubel, Sep 18 2019 *)

vector(30, n, (11*n-7)^4) \\ G. C. Greubel, Sep 18 2019

[(11*n+4)^4 for n in (0..30)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (256 +49345*x +206411*x^2 -92971*x^3 +2401*x^4)/(1-x)^5.
E.g.f.: (256 + 50369*x + 177991*x^2 + 109142*x^3 + 14641*x^4)*exp(x). (End)

Terms a(20) onward added by G. C. Greubel, Sep 18 2019

A017441 a(n) = (11*n + 4)^5.

Original entry on oeis.org

1024, 759375, 11881376, 69343957, 254803968, 714924299, 1680700000, 3486784401, 6590815232, 11592740743, 19254145824, 30517578125, 46525874176, 68641485507, 98465804768, 137858491849, 188956800000

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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), this sequence (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

List([0..20], n-> (11*n+4)^5); # G. C. Greubel, Sep 18 2019

[(11*n+4)^5: n in [0..20]]; // G. C. Greubel, Sep 18 2019

seq((11*n+4)^5, n=0..20); # G. C. Greubel, Sep 18 2019

(11 Range[0,20]+4)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1}, {1024,759375,11881376,69343957,254803968,714924299},20] (* Harvey P. Dale, Jan 30 2017 *)

vector(20, n, (11*n-7)^5) \\ G. C. Greubel, Sep 18 2019

[(11*n+4)^5 for n in (0..20)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (1024 +753231*x +7340486*x^2 +9425846*x^3 +1788726*x^4 +16807*x^5 )/(1-x)^6.
E.g.f.: (1024 +758351*x +5181825*x^2 +5996155*x^3 +1903330*x^4 +161051*x^5)*exp(x). (End)

A017442 a(n) = (11*n + 4)^6.

Original entry on oeis.org

4096, 11390625, 308915776, 2565726409, 12230590464, 42180533641, 117649000000, 282429536481, 606355001344, 1194052296529, 2194972623936, 3814697265625, 6327518887936, 10090298369529, 15557597153344

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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), this sequence (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

List([0..20], n-> (11*n+4)^6); # G. C. Greubel, Sep 18 2019

[(11*n+4)^6: n in [0..20]]; // G. C. Greubel, Sep 18 2019

A017442:=n->(11*n+4)^6; seq(A017442(n), n=0..20); # Wesley Ivan Hurt, Nov 11 2013

(11*Range[0,20]+4)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {4096, 11390625, 308915776, 2565726409, 12230590464, 42180533641, 117649000000}, 20] (* Harvey P. Dale, Feb 18 2012 *)

vector(20, n, (11*n-7)^6) \\ G. C. Greubel, Sep 18 2019

[(11*n+4)^6 for n in (0..20)] # G. C. Greubel, Sep 18 2019

From Harvey P. Dale, Feb 18 2012: (Start)
a(0)=4096, a(1)=11390625, a(2)=308915776, a(3)=2565726409, a(4)=12230590464, a(5)=42180533641, a(6)=117649000000, 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).
G.f.: ((x*(x*(x*(x*(x*(117649*x +33188681) +359208382) +642375742) +229267417) +11361953) +4096)/(1-x)^7). (End)
a(n) = A017437(n)^6. - Michel Marcus, Nov 12 2013
E.g.f.: (4096 +11386529*x +143069311*x^2 +278857810*x^3 +157317545*x^4 +30438639*x^5 +1771561*x^6)*exp(x). - G. C. Greubel, Sep 18 2019

A017443 a(n) = (11*n + 4)^7.

Original entry on oeis.org

16384, 170859375, 8031810176, 94931877133, 587068342272, 2488651484819, 8235430000000, 22876792454961, 55784660123648, 122987386542487, 250226879128704, 476837158203125, 860542568759296, 1483273860320763

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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), this sequence (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

List([0..20], n-> (11*n+4)^7); # G. C. Greubel, Sep 18 2019

[(11*n+4)^7: n in [0..20]]; // G. C. Greubel, Sep 18 2019

seq((11*n+4)^7, n=0..20); # G. C. Greubel, Sep 18 2019

(11*Range[40] -7)^7 (* G. C. Greubel, Sep 18 2019 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{16384,170859375,8031810176,94931877133,587068342272,2488651484819,8235430000000,22876792454961},20] (* Harvey P. Dale, Dec 29 2024 *)

vector(20, n, (11*n-7)^7) \\ G. C. Greubel, Sep 18 2019

[(11*n+4)^7 for n in (0..20)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (16384 +170728303*x +6665393928*x^2 +35460540721*x^3 +42937032016*x^4 +12375175257*x^5 +605631688*x^6 +823543*x^7)/(1-x)^8.
E.g.f.: (16384 +170842991*x +3845053905*x^2 +11891501391*x^3 +10618678070*x^4 +3526372696*x^5 +458834299*x^6 +19487171*x^7)*exp(x). (End)

A017444 a(n) = (11*n + 4)^8.

Original entry on oeis.org

65536, 2562890625, 208827064576, 3512479453921, 28179280429056, 146830437604321, 576480100000000, 1853020188851841, 5132188731375616, 12667700813876161, 28525864220672256, 59604644775390625, 117033789351264256, 218041257467152161, 388379855336079616

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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), this sequence (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

List([0..20], n-> (11*n+4)^8); # G. C. Greubel, Sep 18 2019

[(11*n+4)^8: n in [0..20]]; // G. C. Greubel, Sep 18 2019

seq((11*n+4)^8, n=0..20); # G. C. Greubel, Sep 18 2019

(11*Range[0,20]+4)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36, -9,1}, {65536,2562890625,208827064576,3512479453921, 28179280429056, 146830437604321,576480100000000,1853020188851841,5132188731375616}, 20] (* Harvey P. Dale, Sep 21 2016 *)

vector(20, n, (11*n-7)^8) \\ G. C. Greubel, Sep 18 2019

[(11*n+4)^8 for n in (0..20)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (65536 +2562300801*x +185763408247*x^2 +1725294430213*x^3 +3869465113539*x^4 +2447616620803*x^5 +401274300613*x^6 +10968077367*x^7 +5764801*x^8)/(1-x)^9.
E.g.f.: (65536 +2562825089*x +101850674431*x^2 +482281144422*x^3 +640503062661*x^4 +324861447834*x^5 +70908500586*x^6 +6625638140*x^7 +214358881*x^8)*exp(x). (End)

Terms a(12) onward added by G. C. Greubel, Sep 18 2019

A017445 a(n) = (11*n + 4)^9.

Original entry on oeis.org

262144, 38443359375, 5429503678976, 129961739795077, 1352605460594688, 8662995818654939, 40353607000000000, 150094635296999121, 472161363286556672, 1304773183829244583, 3251948521156637184

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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), this sequence (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

List([0..20], n-> (11*n+4)^9); # G. C. Greubel, Sep 18 2019

[(11*n+4)^9: n in [0..20]]; // G. C. Greubel, Sep 18 2019

seq((11*n+4)^9, n=0..20); # G. C. Greubel, Sep 18 2019

(11*Range[20] -7)^9 (* G. C. Greubel, Sep 18 2019 *)

vector(20, n, (11*n-7)^9) \\ G. C. Greubel, Sep 18 2019

[(11*n+4)^9 for n in (0..20)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (262144 +38440737935*x +5045081881706*x^2 +77396622719912*x^3 +292702580123078*x^4 +341752101417866*x^5 +125993865875030*x^6 +12525368984504*x^7 +197955754298*x^8 +40353607*x^9)/(1-x)^10.
E.g.f.: (262144 +38443097231*x +2676308611185*x^2 +18964759762355*x^3 +36049239596370*x^4 +26212359111477*x^5 +8537070967194*x^6 +1316670195786*x^7 +92603036592*x^8 +2357947691*x^9)*exp(x). (End)

A017446 a(n) = (11*n + 4)^10.

Original entry on oeis.org

1048576, 576650390625, 141167095653376, 4808584372417849, 64925062108545024, 511116753300641401, 2824752490000000000, 12157665459056928801, 43438845422363213824, 134391637934412192049

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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), this sequence (m=10), A017447 (m=11), A017448 (m=12).

List([0..20], n-> (11*n+4)^10); # G. C. Greubel, Sep 18 2019

[(11*n+4)^10: n in [0..20]]; // G. C. Greubel, Sep 18 2019

seq((11*n+4)^10, n=0..20); # G. C. Greubel, Sep 18 2019

(11*Range[0,20]+4)^10 (* Harvey P. Dale, Aug 30 2015 *)

vector(20, n, (11*n-7)^10) \\ G. C. Greubel, Sep 18 2019

[(11*n+4)^10 for n in (0..20)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (1048576 +576638856289*x +134823999028181*x^2 +3287461918700048*x^3 +19699677304461320*x^4 +38310933951284930*x^5 +26248927783563266*x^6 + 6054309522746024*x^7 +381447629946032*x^8 +3567359998885*x^9 +282475249* x^10)/(1-x)^11.
E.g.f.: (1048576 +576649342049*x +70006897960351*x^2 +731135505930170*x^3 +1938975858011665*x^4 +1943070823137213*x^5 +885930917929827*x^6 + 200558066497800*x^7 +23002851520110*x^8 +1261502014685*x^9 +25937424601* x^10)*exp(x). (End)

A017447 a(n) = (11*n + 4)^11.

Original entry on oeis.org

4194304, 8649755859375, 3670344486987776, 177917621779460413, 3116402981210161152, 30155888444737842659, 197732674300000000000, 984770902183611232881, 3996373778857415671808, 13842338707244455781047

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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), this sequence (m=11), A017448 (m=12).

List([0..20], n-> (11*n+4)^11); # G. C. Greubel, Sep 18 2019

[(11*n+4)^11: n in [0..20]]; // G. C. Greubel, Sep 18 2019

seq((11*n+4)^11, n=0..20); # G. C. Greubel, Sep 18 2019

(11Range[0,10]+4)^11 (* Harvey P. Dale, Jun 23 2013 *)

vector(20, n, (11*n-7)^11) \\ G. C. Greubel, Sep 18 2019

[(11*n+4)^11 for n in (0..20)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (4194304 +8649705527727*x +3566547693499340*x^2 +134444370899578971*x^3 +1221731311784947392*x^4 +3698421546351487230*x^5 +4212702849829094280*x^6 +1829094388304154510*x^7 +277265562864875904*x^8 +11429419348320083*x^9 +64244682158316*x^10 +1977326743*x^11)/(1-x)^12.
E.g.f.: (4194304 +8649751665071*x +1826522489731665*x^2 +27822089596980151*x^3 +101113331749791790*x^4 +135969913003223882*x^5 +83388943309597233*x^6 +25990443483549897*x^7 +4322401071325920*x^8 +382966074233765*x^9 +16833388566049*x^10 +285311670611*x^11)*exp(x). (End)

cp's OEIS Frontend

A017437 a(n) = 11*n + 4.

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A017439 a(n) = (11*n + 4)^3.

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A017440 a(n) = (11*n + 4)^4.

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A017441 a(n) = (11*n + 4)^5.

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A017442 a(n) = (11*n + 4)^6.

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A017443 a(n) = (11*n + 4)^7.

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