A017485 -id:A017485 - cp's OEIS frontend

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

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

A017496 a(n) = (11*n + 8)^12.

Original entry on oeis.org

68719476736, 2213314919066161, 531441000000000000, 22563490300366186081, 390877006486250192896, 3909188328478827879681, 26963771415920784510976, 142241757136172119140625, 612709757329767363772416, 2252191588960823337718801

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+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), A017495 (m=11), this sequence (m=12).

List([0..20], n-> (11*n+8)^12); # G. C. Greubel, Sep 22 2019

[(11*n+8)^12: n in [0..20]]; // G. C. Greubel, Sep 22 2019

seq((11*n+8)^12, n=0..20); # G. C. Greubel, Sep 22 2019

(11*Range[0,20]+8)^12 (* Harvey P. Dale, Jul 31 2012 *)

makelist( (11*n+8)^12, n, 0, 30); /* Martin Ettl, Oct 21 2012 */

vector(20, n, (11*n-3)^12) \\ G. C. Greubel, Sep 22 2019

[(11*n+8)^12 for n in (0..20)] # G. C. Greubel, Sep 22 2019

From G. C. Greubel, Sep 22 2019: (Start)
G.f.: (68719476736 +2212421565868593*x +502673266171325315 x^2 + 15827376210283000143*x^3 +138371071649062718037*x^4 + 437329793311303632234*x^5 +556703322340591831614*x^6 + 291323423723258446014*x^7 +59225473544688673002*x^8 + 3967943081254819733*x^9 +58867623955964175*x^10 +56693905466563*x^11 + 531441*x^12)/(1-x)^13.
E.g.f.: (68719476736 +2213246199589425*x +263507219440672207*x^2 + 3495967862733984638*x^3 +12658451587242860861*x^4 +18126123796309288584* x^5 +12400673710435349284*x^6 +4501229025478529124*x^7 + 916653053822529507*x^8 +106739635024880275*x^9 +6967025684650009*x^10 + 234526193242242*x^11 +3138428376721*x^12)*exp(x). (End)

A125199 Triangle read by rows: T(n,k) = 4nk - n - k, 1<=k<=n.

Original entry on oeis.org

2, 5, 12, 8, 19, 30, 11, 26, 41, 56, 14, 33, 52, 71, 90, 17, 40, 63, 86, 109, 132, 20, 47, 74, 101, 128, 155, 182, 23, 54, 85, 116, 147, 178, 209, 240, 26, 61, 96, 131, 166, 201, 236, 271, 306, 29, 68, 107, 146, 185, 224, 263, 302, 341, 380, 32, 75, 118, 161, 204, 247

Offset: 1

Reinhard Zumkeller, Nov 24 2006

A124934 gives the range: for n,k with 1<=k<=n exists at least one m such that A124934(m)=T(n,k);
row sums give A125200; central terms give A125201;
T(n,1) = A016789(n-1);
T(n,2) = A017041(n-1) for n>1;
T(n,3) = A017485(n-1) for n>2;
T(n,n-1) = A125202(n) for n>1;
T(n,n) = A002939(n).

Flatten[Table[4*n*k-n-k,{n,15},{k,n}]] (* Harvey P. Dale, Nov 15 2014 *)

A157442 a(n) = 14641n^2 - 24684n + 10405.

Original entry on oeis.org

362, 19601, 68122, 145925, 253010, 389377, 555026, 749957, 974170, 1227665, 1510442, 1822501, 2163842, 2534465, 2934370, 3363557, 3822026, 4309777, 4826810, 5373125, 5948722, 6553601, 7187762, 7851205, 8543930, 9265937

Offset: 1

Vincenzo Librandi, Mar 01 2009

The identity (14641*n^2 - 24684*n + 10405)^2 - (121*n^2 - 204*n + 86)*(1331*n - 1122)^2 = 1 can be written as a(n)^2 - A157440(n)*A157441(n)^2 = 1. - Vincenzo Librandi, Jan 29 2012

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Vincenzo Librandi, X^2-AY^2=1
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A017485, A157440, A157441.

I:=[362, 19601, 68122]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012

Table[14641n^2-24684n+10405,{n,30}] (* or *) LinearRecurrence[{3,-3,1},{362,19601,68122},30]

for(n=1, 40, print1(14641*n^2 - 24684*n + 10405", ")); \\ Vincenzo Librandi, Jan 29 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=362, a(2)=19601, a(3)=68122. - Harvey P. Dale, Oct 22 2011
G.f.: x*(-10405*x^2 - 18515*x - 362)/(x-1)^3. - Harvey P. Dale, Oct 22 2011
a(n) = A017485(11*n-10)^2 + 1. - Bruno Berselli, Jan 29 2012

A243520 Numbers that are congruent to {0, 8} mod 11.

Original entry on oeis.org

0, 8, 11, 19, 22, 30, 33, 41, 44, 52, 55, 63, 66, 74, 77, 85, 88, 96, 99, 107, 110, 118, 121, 129, 132, 140, 143, 151, 154, 162, 165, 173, 176, 184, 187, 195, 198, 206, 209, 217, 220, 228, 231, 239, 242, 250, 253, 261, 264, 272, 275, 283, 286, 294, 297, 305

Offset: 0

Viet Quoc Le Tran, Jun 14 2014

Union of A008593 and A017485. - Michel Marcus, Jun 15 2014

This sequence mimics in some sense the ceiling function of n/2 (the seq. A110654) relative to variations from a main class of recurrence relations; in order to get the ceiling function of n/2 (see Formula section), the vector v must be [0,1] instead of [3,8]. - R. J. Cano, Jun 15 2014

R. J. Cano, Table of n, a(n) for n = 0..9999
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A010706, A110654, A078707.

&cat [[11*n,11*n+8]: n in [0..30]]; // [Bruno Berselli, Jun 16 2014]

A243520:=n->5*n + 2*(n mod 2) + ceil(n/2); seq(A243520(n), n=0..50); # Wesley Ivan Hurt, Jun 21 2014

Flatten[Table[11 n + {0, 8}, {n, 0, 32}]] (* Alonso del Arte, Jun 15 2014 *)

a(n)=5*n+2*(n%2)+ceil(n/2); \\ R. J. Cano, Jun 15 2014

a(n)=if(!n,0,a(n-1)+[3,8][1+n%2]); \\ R. J. Cano, Jun 15 2014

a(n) = -5/4*(-1)^n + 11*n/2 + 5/4.
From R. J. Cano, Jun 15 2014: (Start)
a(n) = 5*n + 2*(n mod 2) + ceiling(n/2).
If n=0 then a(n) is zero, else a(n) = a(n-1) + v[n mod 2], where v is [3,8]. (End)
G.f.: x*(8 + 3*x) / ((1 + x)*(1 - x)^2). [Bruno Berselli, Jun 16 2014]
a(n) = sum( A010706(i), i=0..n ) - 3. [Bruno Berselli, Jun 16 2014]
E.g.f.: (11*x*exp(x) + 5*sinh(x))/2. - David Lovler, Sep 04 2022

A108725 Numbers n such that 11*n + 19 is prime.

Original entry on oeis.org

0, 2, 8, 12, 14, 20, 24, 30, 44, 48, 50, 54, 62, 72, 78, 90, 92, 98, 104, 110, 122, 128, 132, 134, 140, 150, 162, 164, 168, 170, 174, 180, 188, 192, 194, 212, 218, 230, 234, 240, 252, 258, 260, 272, 282, 288, 290, 294, 300, 308, 318, 320, 324, 332, 344, 348, 362

Offset: 1

Parthasarathy Nambi, Jun 21 2005

All terms must be even. - Harvey P. Dale, Jan 05 2019

			If n=0, then 11*n + 19 = 19 (prime).
If n=48, then 11*n + 19 = 547 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A108233.

Cf. A017485, A141855.

a:=proc(n) if isprime(11*n+19)=true then n else fi end: seq(a(n),n=0..400); # Emeric Deutsch, Jul 04 2005

Select[Range[0,400,2],PrimeQ[ 11#+19]&] (* Harvey P. Dale, Jan 05 2019 *)

is(n)=isprime(11*n+19) \\ Charles R Greathouse IV, Jun 13 2017

More terms from Emeric Deutsch, Jul 04 2005

A248339 a(n) = 22*n + 19.

Original entry on oeis.org

19, 41, 63, 85, 107, 129, 151, 173, 195, 217, 239, 261, 283, 305, 327, 349, 371, 393, 415, 437, 459, 481, 503, 525, 547, 569, 591, 613, 635, 657, 679, 701, 723, 745, 767, 789, 811, 833, 855, 877, 899, 921, 943, 965, 987, 1009

Offset: 0

Karl V. Keller, Jr., Oct 05 2014

These are the odd numbers in A017485.
Solutions to 11^x + 13^x == 17 mod 23.
A141855 is the subsequence of primes.

			For n = 4, 22*4 + 19 = 107.

Karl V. Keller, Jr., Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A017485 (11*n+8), A141855.

[22*n+19: n in [0..60]]; // G. C. Greubel, Nov 13 2024

22*Range[0,50]+19 (* or *) LinearRecurrence[{2,-1},{19,41},50] (* Harvey P. Dale, Dec 20 2014 *)

Vec((3*x+19)/(x-1)^2 + O(x^100)) \\ Colin Barker, Oct 05 2014

for n in range(101):
    print(22*n+19,end=', ')

a(n) = 22*n + 19.
From Colin Barker, Oct 05 2014: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (19 + 3*x) / (1-x)^2. (End)
E.g.f.: (19 + 22*x)*exp(x). - G. C. Greubel, Nov 13 2024

cp's OEIS Frontend

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

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

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

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

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A017496 a(n) = (11*n + 8)^12.

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A125199 Triangle read by rows: T(n,k) = 4*n*k - n - k, 1<=k<=n.

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A125199 Triangle read by rows: T(n,k) = 4nk - n - k, 1<=k<=n.

A157442 a(n) = 14641n^2 - 24684n + 10405.