A008605 -id:A008605 - cp's OEIS frontend

A008606 Multiples of 24.

0, 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408, 432, 456, 480, 504, 528, 552, 576, 600, 624, 648, 672, 696, 720, 744, 768, 792, 816, 840, 864, 888, 912, 936, 960, 984, 1008, 1032, 1056, 1080, 1104, 1128, 1152, 1176, 1200

Offset: 0

N. J. A. Sloane

If n is a multiple of 24, also the sum of the divisors of n-1 is a multiple of 24. - Vincenzo Librandi, Apr 12 2014

This is the sequence of numbers n such that A259748(n)/n = 11/12. - Danny Rorabaugh, Oct 22 2015

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.
Tanya Khovanova, Recursive Sequences.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 336.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008604, A008605.

Range[0, 1500, 24] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
CoefficientList[Series[24 x / (x - 1)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Jun 11 2013 *)

a(n)=24*n \\ Charles R Greathouse IV, Sep 24 2015

G.f.: 24*x/(1-x)^2. - Vincenzo Librandi, Jun 11 2013
a(n) = 24*A001477(n) - Danny Rorabaugh, Oct 24 2015
E.g.f.: 24*x*exp(x). - Stefano Spezia, Mar 02 2025

A008607 Multiples of 25.

Original entry on oeis.org

0, 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 725, 750, 775, 800, 825, 850, 875, 900, 925, 950, 975, 1000, 1025, 1050, 1075, 1100, 1125, 1150, 1175, 1200, 1225

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 337
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008605, A008606.

Range[0, 1500, 25] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
25*Range[0,50] (* Harvey P. Dale, Jul 28 2020 *)

a(n)=25*n \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 25*x/(1-x)^2. - Colin Barker, Feb 19 2012
From Wesley Ivan Hurt, May 19 2024: (Start)
a(n) = 25*n.
a(n) = 2*a(n-1) - a(n-2). (End)
E.g.f.: 25*x*exp(x). - Stefano Spezia, Oct 18 2024

A195819 Multiples of 29.

Original entry on oeis.org

0, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, 377, 406, 435, 464, 493, 522, 551, 580, 609, 638, 667, 696, 725, 754, 783, 812, 841, 870, 899, 928, 957, 986, 1015, 1044, 1073, 1102, 1131, 1160, 1189, 1218, 1247, 1276, 1305, 1334

Offset: 0

Omar E. Pol, Oct 12 2011

Length of hypotenuses on the main diagonal of the Pythagorean spiral whose edges have length A195033 and whose vertices are the numbers A195034, if n >= 1.

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A004922, A004942, A008605, A010868, A135631, A195033, A195034.

29Range[0,50] (* Harvey P. Dale, Oct 25 2011 *)

a(n) = 29*n.
From Elmo R. Oliveira, Mar 21 2024: (Start)
G.f.: 29*x/(x-1)^2.
E.g.f.: 29*x*exp(x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

A244632 a(n) = 23*n^2.

Original entry on oeis.org

0, 23, 92, 207, 368, 575, 828, 1127, 1472, 1863, 2300, 2783, 3312, 3887, 4508, 5175, 5888, 6647, 7452, 8303, 9200, 10143, 11132, 12167, 13248, 14375, 15548, 16767, 18032, 19343, 20700, 22103, 23552, 25047, 26588, 28175, 29808, 31487, 33212, 34983, 36800, 38663

Offset: 0

Vincenzo Librandi, Jul 03 2014

First bisection of A195058. - Bruno Berselli, Jul 03 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000290, A008605, A195058.

Cf. similar sequences listed in A244630.

Magma
```
[23*n^2: n in [0..40]];
```

Table[23 n^2, {n, 0, 40}]
LinearRecurrence[{3,-3,1},{0,23,92},50] (* Harvey P. Dale, Jul 14 2024 *)

a(n)=23*n^2 \\ Charles R Greathouse IV, Jun 17 2017

G.f.: 23*x*(1 + x)/(1 - x)^3. [corrected by Bruno Berselli, Jul 03 2014]
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
a(n) = 23*A000290(n). - Omar E. Pol, Jul 03 2014
From Elmo R. Oliveira, Dec 01 2024: (Start)
E.g.f.: 23*x*(1 + x)*exp(x).
a(n) = n*A008605(n) = A195058(2*n). (End)

A317323 Multiples of 23 and odd numbers interleaved.

Original entry on oeis.org

0, 1, 23, 3, 46, 5, 69, 7, 92, 9, 115, 11, 138, 13, 161, 15, 184, 17, 207, 19, 230, 21, 253, 23, 276, 25, 299, 27, 322, 29, 345, 31, 368, 33, 391, 35, 414, 37, 437, 39, 460, 41, 483, 43, 506, 45, 529, 47, 552, 49, 575, 51, 598, 53, 621, 55, 644, 57, 667, 59, 690, 61, 713, 63, 736, 65, 759, 67, 782, 69

Offset: 0

Omar E. Pol, Jul 25 2018

Partial sums give the generalized 27-gonal numbers (A316725).

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 27-gonal numbers.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A008605 and A005408 interleaved.
Column 23 of A195151.
Sequences whose partial sums give the generalized k-gonal numbers: A026741 (k=5), A001477 (k=6), zero together with A080512 (k=7), A022998 (k=8), A195140 (k=9), zero together with A165998 (k=10), A195159 (k=11), A195161 (k=12), A195312 (k=13), A195817 (k=14).
Cf. A316725.

With[{nn=40},Riffle[23*Range[0,nn],Range[1,2*nn,2]]] (* or *) LinearRecurrence[{0,2,0,-1},{0,1,23,3},80] (* Harvey P. Dale, May 05 2019 *)

concat(0, Vec(x*(1 + 23*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018

a(2n) = 23*n, a(2n+1) = 2*n + 1.
From Colin Barker, Jul 29 2018: (Start)
G.f.: x*(1 + 23*x + x^2) / ((1 - x)^2*(1 + x)^2).
a(n) = 2*a(n-2) - a(n-4) for n>3. (End)
Multiplicative with a(2^e) = 23*2^(e-1), and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023
Dirichlet g.f.: zeta(s-1) * (1 + 21/2^s). - Amiram Eldar, Oct 26 2023

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A008606 Multiples of 24.

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A008607 Multiples of 25.

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A195819 Multiples of 29.

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A244632 a(n) = 23*n^2.

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A317323 Multiples of 23 and odd numbers interleaved.

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