A142150 -id:A142150 - cp's OEIS frontend

A115273 a(n) = floor(n/3)*(n mod 3).

0, 0, 0, 0, 1, 2, 0, 2, 4, 0, 3, 6, 0, 4, 8, 0, 5, 10, 0, 6, 12, 0, 7, 14, 0, 8, 16, 0, 9, 18, 0, 10, 20, 0, 11, 22, 0, 12, 24, 0, 13, 26, 0, 14, 28, 0, 15, 30, 0, 16, 32, 0, 17, 34, 0, 18, 36, 0, 19, 38, 0, 20, 40, 0, 21, 42, 0, 22, 44, 0, 23, 46, 0, 24, 48, 0, 25, 50, 0, 26, 52, 0, 27, 54, 0, 28, 56

Offset: 0

Zak Seidov, Jan 18 2006

Three arithmetic progressions interlaced: a(1)=1,2,0 and d=a(n+1)-a(n)=1,2,0. Cf. A115274(n) = n+a(n), n=1,2,3,...

Cf. A115274.

Cf. A142150 (the base 2 analog), A257844, ..., A257850.

[Floor(n/3)*(n mod 3): n in [0..100]]; // Vincenzo Librandi, May 11 2015

Table[Floor[n/3]*Mod[n, 3], {n, 0, 86}] (* Extended to offset 0 by M. F. Hasler, May 11 2015 *)

a(n, b=3)=(n=divrem(n, b))[1]*n[2] \\ M. F. Hasler, May 10 2015

from math import prod
def A115273(n): return prod(divmod(n,3)) # Chai Wah Wu, Jan 19 2023

a(3*k+1) = k, a(3*k+2) = 2*k, a(3*k+3) = 0, k >= 1.

G.f.: x^4*(2*x+1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, May 11 2015

a(0)-a(3) and cross-references added by M. F. Hasler, May 11 2015

A209297 Triangle read by rows: T(n,k) = k*n + k - n, 1 <= k <= n.

Original entry on oeis.org

1, 1, 4, 1, 5, 9, 1, 6, 11, 16, 1, 7, 13, 19, 25, 1, 8, 15, 22, 29, 36, 1, 9, 17, 25, 33, 41, 49, 1, 10, 19, 28, 37, 46, 55, 64, 1, 11, 21, 31, 41, 51, 61, 71, 81, 1, 12, 23, 34, 45, 56, 67, 78, 89, 100, 1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 1, 14, 27

Offset: 1

Reinhard Zumkeller, Jan 19 2013

From Michel Marcus, May 18 2021: (Start)
The n-th row of the triangle is the main diagonal of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
                                             [1   2  3  4  5]
                             [1   2  3  4]   [6   7  8  9 10]
                   [1 2 3]   [5   6  7  8]   [11 12 13 14 15]
          [1 2]    [4 5 6]   [9  10 11 12]   [16 17 18 19 20]
  [1]     [3 4]    [7 8 9]   [13 14 15 16]   [21 22 23 24 25]
  -----------------------------------------------------------
   1       1 4      1 5 9     1  6  11 16     1  7  13 19 25
(End)

			From _Muniru A Asiru_, Oct 31 2017: (Start)
Triangle begins:
  1;
  1,  4;
  1,  5,  9;
  1,  6, 11, 16;
  1,  7, 13, 19, 25;
  1,  8, 15, 22, 29, 36;
  1,  9, 17, 25, 33, 41, 49;
  1, 10, 19, 28, 37, 46, 55, 64;
  1, 11, 21, 31, 41, 51, 61, 71, 81;
  1, 12, 23, 34, 45, 56, 67, 78, 89, 100;
  ... (End)

Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Cf. A162610; A000012 (left edge), A000290 (right edge), A006003 (row sums), A001844 (central terms), A026741 (number of odd terms per row), A142150 (number of even terms per row), A221490 (number of primes per row).

Flat(List([1..10^3], n -> List([1..n], k -> k * n + k - n))); # Muniru A Asiru, Oct 31 2017

a209297 n k = k * n + k - n
a209297_row n = map (a209297 n) [1..n]
a209297_tabl = map a209297_row [1..]

Array[Range[1, #^2, #+1]&,10] (* Paolo Xausa, Feb 08 2024 *)

T(n,k) = (k-1)*(n+1)+1.

A375924 Number A(n,k) of partitions of [n] such that the element sum of each block is one more than a multiple of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 5, 0, 1, 1, 0, 2, 15, 0, 1, 1, 0, 0, 4, 52, 0, 1, 1, 0, 1, 1, 10, 203, 0, 1, 1, 0, 1, 2, 3, 28, 877, 0, 1, 1, 0, 0, 0, 3, 9, 96, 4140, 0, 1, 1, 0, 0, 0, 0, 1, 17, 320, 21147, 0, 1, 1, 0, 0, 0, 1, 1, 8, 108, 1436, 115975, 0

Offset: 0

Alois P. Heinz, Sep 02 2024

			A(5,2) = 10: 12345, 124|3|5, 12|34|5, 12|3|45, 14|23|5, 1|234|5, 1|23|45, 14|25|3, 1|245|3, 1|25|34.
A(6,3) = 9: 136|25|4, 13|256|4, 13|25|46, 16|235|4, 1|2356|4, 1|235|46, 16|25|34, 1|256|34, 1|25|346.
A(7,4) = 8: 14|23|5|67, 1|234|5|67, 1|23|45|67, 1|23|467|5, 14|27|36|5, 1|247|36|5, 1|27|346|5, 1|27|36|45.
A(8,5) = 1: 12345678.
A(8,8) = 4: 18|27|36|45, 1|278|36|45, 1|27|368|45, 1|27|36|458.
A(9,6) = 87: 123469|58|7, 12349|568|7, 12349|58|67, 123568|49|7, ..., 1|25|346789, 16|289|3457, 1|2689|3457, 1|289|34567.
A(9,8) = 5: 18|27|36|45|9, 1|278|36|45|9, 1|27|368|45|9, 1|27|36|458|9, 1|27|36|45|89.
A(9,10) = 1: 1|29|38|47|56.
Square array A(n,k) begins:
  1,      1,    1,    1,   1,  1,  1,  1, 1, 1, 1, ...
  1,      1,    1,    1,   1,  1,  1,  1, 1, 1, 1, ...
  0,      2,    1,    0,   0,  0,  0,  0, 0, 0, 0, ...
  0,      5,    2,    0,   1,  1,  0,  0, 0, 0, 0, ...
  0,     15,    4,    1,   2,  0,  0,  0, 1, 1, 0, ...
  0,     52,   10,    3,   3,  0,  1,  1, 0, 0, 0, ...
  0,    203,   28,    9,   1,  1,  3,  0, 0, 1, 1, ...
  0,    877,   96,   17,   8, 15,  4,  0, 1, 1, 0, ...
  0,   4140,  320,  108,  32,  1,  0,  1, 4, 0, 0, ...
  0,  21147, 1436,  324,  51, 10, 87, 72, 5, 0, 1, ...
  0, 115975, 5556, 1409, 621, 50,  1,  0, 0, 1, 5, ...

Alois P. Heinz, Antidiagonals n = 0..40, flattened
Wikipedia, Partition of a set

Columns k=0-10 give: A019590(n+1), A000110, A369079, A374692, A375939, A375940, A375941, A375942, A375943, A375944, A375957.
Rows n=1-2 give: A000012, A033322 (for k>=1).
Main diagonal gives A142150 (for n>=2).
A(n+1,n) gives A158416 (for n>=2).
A(n,n+1) gives A135528(n+1).

A237420 If n is odd, then a(n) = 0; otherwise, a(n) = n.

Original entry on oeis.org

0, 0, 2, 0, 4, 0, 6, 0, 8, 0, 10, 0, 12, 0, 14, 0, 16, 0, 18, 0, 20, 0, 22, 0, 24, 0, 26, 0, 28, 0, 30, 0, 32, 0, 34, 0, 36, 0, 38, 0, 40, 0, 42, 0, 44, 0, 46, 0, 48, 0, 50, 0, 52, 0, 54, 0, 56, 0, 58, 0, 60, 0, 62, 0, 64, 0, 66, 0, 68, 0, 70, 0, 72, 0, 74

Offset: 0

Vincenzo Librandi, Feb 24 2014

Normally the OEIS excludes sequences in which every other term is zero. But there are exceptions for especially important sequences like this one. - N. J. A. Sloane, Feb 27 2014
Essentially the factorial expansion of exp(-1): exp(-1) = Sum_{n>=1} a(n)/(n+1)!. - Joerg Arndt, Mar 13 2014
a(n) is the number of m < n for which a(m) has the same parity as n. For instance, a(4) = 4 because 4 has the same parity as a(0), a(1), a(2), and a(3). - Alec Jones, May 16 2016
This sequence is an example of a sequence that has no limit while the Cesàro means limit is infinite. See A354280 for further information. - Bernard Schott, May 22 2022

J. M. Arnaudiès, P. Delezoide et H. Fraysse, Exercices résolus d'Analyse du cours de mathématiques - 2, Dunod, Exercice 10, pp. 14-16.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (corrected by Ray Chandler, Jan 19 2019).
ProofWiki, Cesàro mean.
Wikipedia, Ernesto Cesàro.
Wikipédia, Lemme de Cesàro (in French).
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A005843, A110660, A142150, A193356, A354280.

About the Cesàro mean theorem: A033999, A114112.

[IsOdd(n) select 0 else n: n in [1..80]];

Magma
```
[(1+(-1)^n)*n/2: n in [1..80]];
```

&cat [[n, 0]: n in [0..80 by 2]]; // Bruno Berselli, Nov 11 2016

seq(op([0,2*i]),i=1..30); # Robert Israel, Aug 27 2015

Table[If[OddQ[n], 0, n], {n, 80}]
CoefficientList[Series[2 x /(1 - x^2)^2, {x, 0, 80}], x]
LinearRecurrence[{0, 2, 0, -1}, {0, 0, 2, 0}, 75] (* Robert G. Wilson v, Nov 11 2016 *)
Riffle[Range[0,80,2],0] (* Harvey P. Dale, Mar 16 2021 *)

a(n)=if(n%2==0,n,0) \\ Anders Hellström, Aug 27 2015

def a(n): return 0 if n%2 else n # Michael S. Branicky, Jun 05 2022

O.g.f.: 2*x^2/(1-x^2)^2.
E.g.f.: x*sinh(x). - Robert Israel, Aug 27 2015
a(n) = 2*a(n-2) - a(n-4) for n>4.
a(n) = 2*A142150(n) = (1+(-1)^n)*n/2 = n*((n-1) mod 2).
a(n) = floor(n^(-1)^n) for n>1. - Ilya Gutkovskiy, Aug 27 2015
Sum_{i=1..n} a(i) = A110660(n). - Bruno Berselli, Feb 27 2014
a(n) = -1 + ceiling((n + 1)^(sin(Pi*n/2) + cos(Pi*n))). - Lechoslaw Ratajczak, Nov 06 2016

Edited by Bruno Berselli, Feb 27 2014

A257844 a(n) = floor(n/4) * (n mod 4).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 3, 0, 2, 4, 6, 0, 3, 6, 9, 0, 4, 8, 12, 0, 5, 10, 15, 0, 6, 12, 18, 0, 7, 14, 21, 0, 8, 16, 24, 0, 9, 18, 27, 0, 10, 20, 30, 0, 11, 22, 33, 0, 12, 24, 36, 0, 13, 26, 39, 0, 14, 28, 42, 0, 15, 30, 45, 0, 16, 32, 48, 0, 17, 34, 51, 0, 18, 36

Offset: 0

M. F. Hasler, May 10 2015

Equivalently, write n in base 4, multiply the last digit by the number with its last digit removed.

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

Cf. A142150 (the base-2 analog), A115273, A257845 - A257850.

[Floor(n/4)*(n mod 4) : n in [0..100]]; // Wesley Ivan Hurt, Jun 22 2015

I:=[0,0,0,0,0,1,2,3]; [n le 8 select I[n] else 2*Self(n-4)-Self(n-8): n in [1..100]]; // Vincenzo Librandi, Jun 23 2015

A257844:=n->floor(n/4)*(n mod 4): seq(A257844(n), n=0..100); # Wesley Ivan Hurt, Jun 22 2015

Table[Floor[n/4] Mod[n, 4], {n, 0, 100}] (* Wesley Ivan Hurt, Jun 22 2015 *)

PARI
```
a(n,b=4)=(n=divrem(n,b))[1]*n[2]
```

concat([0,0,0,0,0], Vec(x^5*(3*x^2+2*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)^2) + O(x^100))) \\ Colin Barker, May 11 2015

def A257844(n): return (n>>2)*(n&3) # Chai Wah Wu, Jan 27 2023

a(n) = 2*a(n-4) - a(n-8), n > 8. - Colin Barker, May 11 2015
G.f.: x^5*(3*x^2+2*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - Colin Barker, May 11 2015
a(n) = (3 - 2*(-1)^((2*n - 1 + (-1)^n)/4) - (-1)^n)*(2*n - 3 + 2*(-1)^((2*n - 1 + (-1)^n)/4) + (-1)^n)/16. - Wesley Ivan Hurt, Jun 22 2015

A195034 Vertex number of a square spiral in which the length of the first two edges are the legs of the primitive Pythagorean triple [21, 20, 29]. The edges of the spiral have length A195033.

Original entry on oeis.org

0, 21, 41, 83, 123, 186, 246, 330, 410, 515, 615, 741, 861, 1008, 1148, 1316, 1476, 1665, 1845, 2055, 2255, 2486, 2706, 2958, 3198, 3471, 3731, 4025, 4305, 4620, 4920, 5256, 5576, 5933, 6273, 6651, 7011, 7410, 7790, 8210, 8610, 9051, 9471

Offset: 0

Omar E. Pol, Sep 12 2011

Zero together with partial sums of A195033.
The only primes in the sequence are 41 and 83 since a(n) = (1/2)*((2*n+(-1)^n+3)/4)*((82*n-43*(-1)^n+43)/4). - Bruno Berselli, Oct 12 2011
The spiral contains infinitely many Pythagorean triples in which the hypotenuses on the main diagonal are the positives multiples of 29 (Cf. A195819). The vertices on the main diagonal are the numbers A195038 = (21+20)*A000217 = 41*A000217, where both 21 and 20 are the first two edges in the spiral. The distance "a" between nearest edges that are perpendicular to the initial edge of the spiral is 21, while the distance "b" between nearest edges that are parallel to the initial edge is 20, so the distance "c" between nearest vertices on the same axis is 29 because from the Pythagorean theorem we can write c = (a^2+b^2)^(1/2) = sqrt(21^2+20^2) = sqrt(441+400) = sqrt(841) = 29. - Omar E. Pol, Oct 12 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Ron Knott, Pythagorean triangles and Triples
Eric Weisstein's World of Mathematics, Pythagorean Triple
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Cf. A195020, A195032, A195033, A195036, A195038.

[(2*n*(41*n+83)-(2*n+43)*(-1)^n+43)/16: n in [0..50]]; // Vincenzo Librandi, Oct 14 2011

LinearRecurrence[{1,2,-2,-1,1},{0,21,41,83,123},50] (* Harvey P. Dale, May 02 2012 *)

concat(0, Vec(x*(21+20*x)/((1+x)^2*(1-x)^3) + O(x^60))) \\ Michel Marcus, Mar 08 2016

From Bruno Berselli, Oct 12 2011: (Start)
G.f.: x*(21+20*x)/((1+x)^2*(1-x)^3).
a(n) = (2*n*(41*n+83)-(2*n+43)*(-1)^n+43)/16.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5).
a(n)-a(-n-2) = A142150(n+1). (End)

A142151 a(n) = OR{k XOR (n-k): 0<=k<=n}.

Original entry on oeis.org

0, 1, 2, 3, 6, 5, 6, 7, 14, 13, 14, 11, 14, 13, 14, 15, 30, 29, 30, 27, 30, 29, 30, 23, 30, 29, 30, 27, 30, 29, 30, 31, 62, 61, 62, 59, 62, 61, 62, 55, 62, 61, 62, 59, 62, 61, 62, 47, 62, 61, 62, 59, 62, 61, 62, 55, 62, 61, 62, 59, 62, 61, 62, 63, 126, 125, 126, 123, 126, 125

Offset: 0

Reinhard Zumkeller, Jul 15 2008

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Reinhard Zumkeller, Logical Convolutions

Cf. A003817, A000004, A142149, A086099, A142150, A001477, A089633.

import Data.Bits (xor, (.|.))
a142151 :: Integer -> Integer
a142151 = foldl (.|.) 0 . zipWith xor [0..] . reverse . enumFromTo 1
-- Reinhard Zumkeller, Mar 31 2015

using IntegerSequences
A142151List(len) = [Bits("CIMP", n, n+1) for n in 0:len]
println(A142151List(69))  # Peter Luschny, Sep 25 2021

A142151 := n -> n + Bits:-Nor(n, n+1):
seq(A142151(n), n=0..69); # Peter Luschny, Sep 26 2019

from functools import reduce
from operator import or_
def A142151(n): return 0 if n == 0 else reduce(or_,(k^n-k for k in range(n+1))) if n % 2 else (1 << n.bit_length()-1)-1 <<1 # Chai Wah Wu, Jun 30 2022

a(2*n) = 2*(A062383(n)-1);

A023416(a(n)) <= 1.

A242480 a(n) = (n*(n+1)/2) mod n + sigma(n) mod n + antisigma(n) mod n.

Original entry on oeis.org

0, 2, 3, 8, 5, 6, 7, 16, 9, 20, 11, 12, 13, 28, 15, 32, 17, 18, 19, 20, 21, 44, 23, 24, 25, 52, 27, 28, 29, 30, 31, 64, 33, 68, 35, 72, 37, 76, 39, 40, 41, 42, 43, 88, 45, 92, 47, 96, 49, 100, 51, 104, 53, 54, 55, 56, 57, 116, 59, 120, 61, 124, 63, 128, 65, 66

Offset: 1

Jaroslav Krizek, May 16 2014

nonn

a(n) / n = 1 for numbers n from A242482, a(n) / n = 2 for numbers n from A242483.
If there are any odd multiply-perfect numbers n > 1 then a(n) = 0.
Possible values of a(n) in increasing order = A242485. Numbers m such that a(n) = m has no solution = A242486.

			a(8) = (8*(8+1)/2) mod 8 + sigma(8) mod 8 + antisigma(8) mod 8 = 36 mod 8 + 15 mod 8 + 21 mod 8 = 4 + 7 + 5 = 16.

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Cf. A242481, A242482, A242483, A242484, A242485, A242486.

[((n*(n+1)div 2 mod n + SumOfDivisors(n) mod n + (n*(n+1)div 2-SumOfDivisors(n)) mod n)): n in [1..1000]]

a(n) = A142150(n) + A054024(n) + A229110(n) = (A000217(n) mod n) + (A000203(n) mod n) + (A024816(n) mod n).

a(n) = A242481(n) * n.

A242481 a(n) = ((n*(n+1)/2) mod n + sigma(n) mod n + antisigma(n) mod n) / n.

Original entry on oeis.org

0, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1

Offset: 1

Jaroslav Krizek, May 16 2014

nonn

a(1) = 0. If there is no odd multiply-perfect number then a(n) = 1 or 2 for n >= 2. See A242482 = numbers m such that a(n) = 1, A242483 = numbers m such that a(n) = 2. If there are any odd multiply-perfect numbers m > 1 then a(m) = 0.

			a(8) = [(8*(8+1)/2) mod 8 + sigma(8) mod 8 + antisigma(8) mod 8] / 8 = (36 mod 8 + 15 mod 8 + 21 mod 8) / 8 = (4 + 7 + 5 ) / 8 = 2.

Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Cf. A242480, A242482, A242483, A242484, A242485, A242486.

[((n*(n+1)div 2 mod n + SumOfDivisors(n) mod n + (n*(n+1)div 2-SumOfDivisors(n)) mod n))div n: n in [1..1000]]

a(n) = (A142150(n) + A054024(n) + A229110(n)) / n = ((A000217(n) mod n) + (A000203(n) mod n) + (A024816(n) mod n)) / n.

a(n) = A242480(n) / n.

A242482 Numbers n such that A242481(n) = ((n*(n+1)/2) mod n + sigma(n) mod n + antisigma(n) mod n) / n = 1.

Original entry on oeis.org

2, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 20, 21, 23, 24, 25, 27, 28, 29, 30, 31, 33, 35, 37, 39, 40, 41, 42, 43, 45, 47, 49, 51, 53, 54, 55, 56, 57, 59, 61, 63, 65, 66, 67, 69, 70, 71, 73, 75, 77, 78, 79, 80, 81, 83, 85, 87, 88, 89, 91, 93, 95, 97, 99

Offset: 1

Jaroslav Krizek, May 16 2014

nonn

Numbers n such that A242480(n) = (1/2*n*(n+1)) mod n + sigma(n) mod n + antisigma(n) mod n = (A142150(n) + A054024(n) + A229110(n)) = ((A000217(n) mod n) + (A000203(n) mod n) + (A024816(n) mod n)) = n. Numbers n such that A242481(n) = (A142150(n) + A054024(n) + A229110(n)) / n = ((A000217(n) mod n) + (A000203(n) mod n) + (A024816(n) mod n)) / n = 1.
Conjecture: with number 1 complement of A242483.
Supersequence of primes (A000040).
If there is no odd multiply-perfect number, then:
(1) a(n) = union of odd numbers >= 3 and even numbers from A239719.
(2) a(n) = supersequence of odd numbers (A005408).

			6 is in sequence because [(6*(6+1)/2) mod 6 + sigma(6) mod 6 + antisigma(6) mod 6] / 6 = (21 mod 6 + 12 mod 6 + 9 mod 6) / 6 = (3 + 0 + 3 ) / 6 = 1.

Jaroslav Krizek, Table of n, a(n) for n = 1..5000

Cf. A242480, A242481, A242483, A242484, A242485, A242486.

[n: n in [1..1000] | n eq ((n*(n+1)div 2 mod n + SumOfDivisors(n) mod n + (n*(n+1)div 2-SumOfDivisors(n)) mod n))]

cp's OEIS Frontend

A115273 a(n) = floor(n/3)*(n mod 3).

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A209297 Triangle read by rows: T(n,k) = k*n + k - n, 1 <= k <= n.

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A375924 Number A(n,k) of partitions of [n] such that the element sum of each block is one more than a multiple of k; square array A(n,k), n>=0, k>=0, read by antidiagonals.

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A237420 If n is odd, then a(n) = 0; otherwise, a(n) = n.

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A257844 a(n) = floor(n/4) * (n mod 4).

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A195034 Vertex number of a square spiral in which the length of the first two edges are the legs of the primitive Pythagorean triple [21, 20, 29]. The edges of the spiral have length A195033.

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