cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 12 results. Next

A017461 a(n) = 11*n + 6.

Original entry on oeis.org

6, 17, 28, 39, 50, 61, 72, 83, 94, 105, 116, 127, 138, 149, 160, 171, 182, 193, 204, 215, 226, 237, 248, 259, 270, 281, 292, 303, 314, 325, 336, 347, 358, 369, 380, 391, 402, 413, 424, 435, 446, 457, 468, 479, 490, 501, 512, 523, 534, 545, 556, 567, 578, 589
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A008593, A017401, A017449, A141694.
Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.
Powers of the form (11*n+6)^m: this sequence (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), A017471 (m=11), A017472 (m=12).

Programs

Formula

a(0)=6, a(1)=17; for n>1, a(n) = 2*a(n-1) - a(n-2). - Harvey P. Dale, Apr 14 2015
From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (6 + 5*x)/(1-x)^2.
E.g.f.: (6 + 11*x)*exp(x). (End)
a(n) = A141694(n)/2. - Elmo R. Oliveira, Apr 11 2025

A017449 a(n) = 11*n + 5.

Original entry on oeis.org

5, 16, 27, 38, 49, 60, 71, 82, 93, 104, 115, 126, 137, 148, 159, 170, 181, 192, 203, 214, 225, 236, 247, 258, 269, 280, 291, 302, 313, 324, 335, 346, 357, 368, 379, 390, 401, 412, 423, 434, 445, 456, 467, 478, 489, 500, 511, 522, 533, 544, 555, 566, 577, 588
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A008593, A017401, A017437.
Powers of the form (11*n+5)^m: this sequence (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

Programs

Formula

From G. C. Greubel, Sep 18 2019: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (5 + 6*x)/(1-x)^2.
E.g.f.: (5 + 11*x)*exp(x). (End)

A017509 a(n) = 11*n + 10.

Original entry on oeis.org

10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 120, 131, 142, 153, 164, 175, 186, 197, 208, 219, 230, 241, 252, 263, 274, 285, 296, 307, 318, 329, 340, 351, 362, 373, 384, 395, 406, 417, 428, 439, 450, 461, 472, 483, 494, 505, 516, 527, 538, 549, 560, 571, 582
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

If k is any member of A045572, the sequence lists the numbers n such that (n^k+1)/11 is a nonnegative integer. See also A267541. - Bruno Berselli, Jan 16 2016

Links

Crossrefs

Cf. A008593, A017401, A017413, A045572, A267541.
Cf. A211013 (partial sums), A254322 (partial products).
Powers of the form (11*n+10)^m: this sequence (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).
Cf. A008591, A005408.

Programs

Formula

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (10 + x)/(1-x)^2.
E.g.f.: (10 + 11*x)*exp(x).
a(n) = 2*a(n-1) - a(n-2). (End)
a(n) = A008591(n+1) + A005408(n). - Leo Tavares, Oct 25 2022

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

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).

Programs

Formula

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

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

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).

Programs

Formula

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)

A017413 a(n) = 11*n + 2.

Original entry on oeis.org

2, 13, 24, 35, 46, 57, 68, 79, 90, 101, 112, 123, 134, 145, 156, 167, 178, 189, 200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310, 321, 332, 343, 354, 365, 376, 387, 398, 409, 420, 431, 442, 453, 464, 475, 486, 497, 508, 519, 530, 541, 552, 563, 574, 585
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A008593, A017401, A017425.

Programs

Formula

From G. C. Greubel, Nov 11 2018: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (2 + 9*x)/(1 - x)^2.
E.g.f.: (2 + 11*x)*exp(x). (End)

A017425 a(n) = 11*n + 3.

Original entry on oeis.org

3, 14, 25, 36, 47, 58, 69, 80, 91, 102, 113, 124, 135, 146, 157, 168, 179, 190, 201, 212, 223, 234, 245, 256, 267, 278, 289, 300, 311, 322, 333, 344, 355, 366, 377, 388, 399, 410, 421, 432, 443, 454, 465, 476, 487, 498, 509, 520, 531, 542, 553, 564, 575, 586
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A008593, A017401, A017413, A226492.

Programs

Formula

From Elmo R. Oliveira, Apr 03 2024: (Start)
G.f.: (3+8*x)/(1-x)^2.
E.g.f.: exp(x)*(3 + 11*x).
a(n) = A226492(n+1) - A226492(n).
a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

Extensions

Terms corrected by Vincenzo Librandi, Sep 02 2011

A001536 a(n) = (11*n+1)*(11*n+10).

Original entry on oeis.org

10, 252, 736, 1462, 2430, 3640, 5092, 6786, 8722, 10900, 13320, 15982, 18886, 22032, 25420, 29050, 32922, 37036, 41392, 45990, 50830, 55912, 61236, 66802, 72610, 78660, 84952, 91486, 98262, 105280, 112540, 120042, 127786, 135772, 144000, 152470, 161182, 170136
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A017401, A017509.

Programs

Formula

a(n) = 242*n + a(n-1) with a(0)=10. - Vincenzo Librandi, Nov 12 2010
G.f.: -2*(5+111*x+5*x^2)/(x-1)^3. - R. J. Mathar, May 30 2022
From Amiram Eldar, Feb 20 2023: (Start)
a(n) = A017401(n)*A017509(n).
Sum_{n>=0} 1/a(n) = cot(Pi/11)*Pi/99.
Product_{n>=0} (1 - 1/a(n)) = cosec(Pi/11)*cos(sqrt(85)*Pi/22).
Product_{n>=0} (1 + 1/a(n)) = cosec(Pi/11)*cos(sqrt(77)*Pi/22). (End)
From Elmo R. Oliveira, Oct 25 2024: (Start)
E.g.f.: exp(x)*(10 + 121*x*(2 + x)).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A050491 a(n) = C(n)*(12n+1) where C(n) = Catalan numbers (A000108).

Original entry on oeis.org

1, 13, 50, 185, 686, 2562, 9636, 36465, 138710, 529958, 2032316, 7818538, 30161740, 116635300, 451980360, 1754766945, 6824030310, 26577181950, 103647597900, 404703270510, 1581953021220, 6189965556060, 24242879364600, 95027512981050, 372782298576636, 1463445866837052
Offset: 0

Views

Author

Barry E. Williams, Dec 27 1999

Keywords

References

  • Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

Crossrefs

Column k=12 of A330965.
Cf. A017401, A027810, A000108.

Programs

  • Magma
    [Catalan(n)*(12*n+1):n in [0..25] ]; // Marius A. Burtea, Jan 05 2020
  • Mathematica
    Table[CatalanNumber[n] * (12*n + 1), {n, 0, 25}] (* Amiram Eldar, Jul 08 2023 *)

Formula

G.f.: (11 - 20*x - 11*sqrt(1 - 4*x))/(2*x*sqrt(1 - 4*x)). - Amiram Eldar, Jul 08 2023

Extensions

Terms a(21) and beyond from Andrew Howroyd, Jan 05 2020

A267755 Expansion of (1 + 2*x + x^2 + x^3 + 4*x^4 + 2*x^5)/(1 - x - x^5 + x^6).

Original entry on oeis.org

1, 3, 4, 5, 9, 12, 14, 15, 16, 20, 23, 25, 26, 27, 31, 34, 36, 37, 38, 42, 45, 47, 48, 49, 53, 56, 58, 59, 60, 64, 67, 69, 70, 71, 75, 78, 80, 81, 82, 86, 89, 91, 92, 93, 97, 100, 102, 103, 104, 108, 111, 113, 114, 115, 119, 122, 124, 125, 126, 130, 133, 135, 136, 137
Offset: 0

Views

Author

Bruno Berselli, Jan 20 2016

Keywords

Comments

(m^k-1)/11 is a nonnegative integer when
. m is a member of this sequence and k is an odd multiple of 5 (A017329),
. m is a member of A017401 and k is odd but not multiple of 5 (A045572),
. m is a member of A175885 and k is even but not multiple of 5 (A217562),
. m is a member of A160542 and k is a positive multiple of 10 (A008592),
apart from the trivial case in which k=0.
Also, numbers that are congruent to {1, 3, 4, 5, 9} mod 11. Therefore, the product of two terms belongs to the sequence.
Union of this sequence and A267541 is A160542.
a(n) is prime for n = 1, 3, 10, 14, 17, 21, 24, 27, 30, 33, 40, 44, 47, ...

Examples

			From the linear recurrence:
(-A267541) ..., -13, -10, -8, -7, -6, -2, 1, 3, 4, 5, 9, 12, ... (A267755)

Links

Crossrefs

Cf. A160542, A017329, A267541.
Related sequences (see the first comment): A017401, A160542, A175885.

Programs

  • Magma
    m:=70; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x+x^2+x^3+4*x^4+2*x^5)/(1-x-x^5+x^6)));
  • Magma
    I:=[1,3,4,5,9,12]; [n le 6 select I[n] else Self(n-1)+Self(n-5)-Self(n-6): n in [1..70]]; // Vincenzo Librandi, Jan 21 2016
  • Maple
    gf := (1 + 2*x + x^2 + x^3 + 4*x^4 + 2*x^5)/(1 - x - x^5 + x^6): deg := 64: series(gf, x, deg): seq(coeff(%, x, n), n=0..deg-1); # Peter Luschny, Jan 21 2016
  • Mathematica
    CoefficientList[Series[(1 + 2 x + x^2 + x^3 + 4 x^4 + 2 x^5)/(1 - x - x^5 + x^6), {x, 0, 70}], x]
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 3, 4, 5, 9, 12}, 70]
Select[Range[140], MemberQ[{1, 3, 4, 5, 9}, Mod[#, 11]]&]
  • PARI
    Vec((1+2*x+x^2+x^3+4*x^4+2*x^5)/(1-x-x^5+x^6)+O(x^70))
  • Sage
    gf = (1 + 2*x + x^2 + x^3 + 4*x^4 + 2*x^5)/(1 - x - x^5 + x^6)
print(taylor(gf, x, 0, 63).list()) # Peter Luschny, Jan 21 2016

Formula

G.f.: (1 + 2*x + x^2 + x^3 + 4*x^4 + 2*x^5)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).
a(n) = a(n-1) + a(n-5) - a(n-6).
a(-n) = -A267541(n-1).
a(n) = n + 1 + 2*floor(n/5) + 3*floor((n+1)/5) + floor((n+4)/5). - Ridouane Oudra, Sep 06 2023
Showing 1-10 of 12 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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