A008589 -id:A008589 - cp's OEIS frontend

A084968 Multiples of 7 coprime to 30.

7, 49, 77, 91, 119, 133, 161, 203, 217, 259, 287, 301, 329, 343, 371, 413, 427, 469, 497, 511, 539, 553, 581, 623, 637, 679, 707, 721, 749, 763, 791, 833, 847, 889, 917, 931, 959, 973, 1001, 1043, 1057, 1099, 1127, 1141, 1169, 1183, 1211, 1253, 1267, 1309

Offset: 1

Robert G. Wilson v, Jun 15 2003

Numbers 7*k such that gcd(k,30) = 1.

Numbers congruent to 7, 49, 77, 91, 119, 133, 161, 203 modulo 210. - Jianing Song, Nov 18 2022

			77 is in the sequence because gcd(77, 30) = 1.
84 is not in the sequence because gcd(84, 3) = 6.
91 is in the sequence because gcd(91, 30) = 1.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Subsequence of A008589.
Fourth row of A083140.
Cf. A084967 (5), A084969 (11), A084970 (13), A332799 (17), A332798 (19), A332797 (23), A007775 (7-rough numbers).

q:= k-> igcd(k, 30)=1:
select(q, [7*i$i=1..300])[];  # Alois P. Heinz, Feb 25 2020

7Select[ Range[190], GCD[ #, 2*3*5] == 1 & ]

is(n)=gcd(210,n)==7 \\ Charles R Greathouse IV, Aug 05 2013

G.f.: 7*x*(x^8 + 6*x^7 + 4*x^6 + 2*x^5 + 4*x^4 + 2*x^3 + 4*x^2 + 6*x + 1) / ((x-1)^2*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Feb 24 2013
Lim_{n->oo} a(n)/n = A038111(4)/A038110(4) = 105/4. - Vladimir Shevelev, Jan 20 2015
a(n) = 7*A007775(n).
a(n+8) = a(n) + 210. - Jianing Song, Nov 18 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(23 + sqrt(5) - sqrt(6*(5 + sqrt(5))))*Pi/105. - Amiram Eldar, Jul 15 2023

A109720 Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1

Offset: 0

Bruce Corrigan (scentman(AT)myfamily.com), Aug 09 2005

This sequence also represents n^12 mod 7; n^18 mod 7; (exponents are = 0 mod 6).
Characteristic sequence for numbers n>=1 to be relatively prime to 7. - Wolfdieter Lang, Oct 29 2008
a(n+4), n>=0, (periodic 1,1,1,0,1,1,1) is also the characteristic sequence for mod m reduced positive odd numbers (i.e., gcd(2*n+1,m)=1, n>=0) for each modulus m from 7*A003591 = [7,14,28,49,56,98,112,196,...]. [Wolfdieter Lang, Feb 04 2012]

Index entries for characteristic functions - _Reinhard Zumkeller_, Nov 30 2009
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1)

Cf. A010876 = n mod 7; A053879 = n^2 mod 7; A070472 = m^3 mod 7; A070512 = n^4 mod 7; A070593 = n^5 mod 7.

Cf. A168185, A145568, A168184, A168182, A168181, A097325, A011558, A166486, A011655, A000035.

PadRight[{},120,{0,1,1,1,1,1,1}] (* Harvey P. Dale, Jul 09 2018 *)

a(n)=n^6%7 \\ Charles R Greathouse IV, Sep 24 2015

[power_mod(n,6,7)for n in range(0, 105)] # Zerinvary Lajos, Nov 06 2009

a(n) = 0 if n=0 mod 7; a(n)= 1 else.
G.f. = (x+x^2+x^3+x^4+x^5+x^6)/(1-x^7)= -x*(1+x)*(1+x+x^2)*(x^2-x+1) / ( (x-1)*(1+x+x^2+x^3+x^4+x^5+x^6) ).
a(n)=1-A082784(n); a(A047304(n))=1; a(A008589(n))=0; A033439(n) = SUM(a(k)*(n-k): 0<=k<=n). - Reinhard Zumkeller, Nov 30 2009
Multiplicative with a(p) = (if p=7 then 0 else 1), p prime. - Reinhard Zumkeller, Nov 30 2009
Dirichlet g.f. (1-7^(-s))*zeta(s). - R. J. Mathar, Mar 06 2011
For the general case: the characteristic function of numbers that are not multiples of m is a(n)=floor((n-1)/m)-floor(n/m)+1, m,n > 0. - Boris Putievskiy, May 08 2013

A141419 Triangle read by rows: T(n, k) = A000217(n) - A000217(n - k) with 1 <= k <= n.

Original entry on oeis.org

1, 2, 3, 3, 5, 6, 4, 7, 9, 10, 5, 9, 12, 14, 15, 6, 11, 15, 18, 20, 21, 7, 13, 18, 22, 25, 27, 28, 8, 15, 21, 26, 30, 33, 35, 36, 9, 17, 24, 30, 35, 39, 42, 44, 45, 10, 19, 27, 34, 40, 45, 49, 52, 54, 55

Offset: 1

Roger L. Bagula, Aug 05 2008

As a rectangle, the accumulation array of A051340.
From Clark Kimberling, Feb 05 2011: (Start)
Here all the weights are divided by two where they aren't in Cahn.
As a rectangle, A141419 is in the accumulation chain
... < A051340 < A141419 < A185874 < A185875 < A185876 < ...
(See A144112 for the definition of accumulation array.)
row 1: A000027
col 1: A000217
diag (1,5,...): A000326 (pentagonal numbers)
diag (2,7,...): A005449 (second pentagonal numbers)
diag (3,9,...): A045943 (triangular matchstick numbers)
diag (4,11,...): A115067
diag (5,13,...): A140090
diag (6,15,...): A140091
diag (7,17,...): A059845
diag (8,19,...): A140672
(End)
Let N=2*n+1 and k=1,2,...,n. Let A_{N,n-1} = [0,...,0,1; 0,...,0,1,1; ...; 0,1,...,1; 1,...,1], an n X n unit-primitive matrix (see [Jeffery]). Let M_n=[A_{N,n-1}]^4. Then t(n,k)=[M_n](1,k), that is, the n-th row of the triangle is given by the first row of M_n. - _L. Edson Jeffery, Nov 20 2011
Conjecture. Let N=2*n+1 and k=1,...,n. Let A_{N,0}, A_{N,1}, ..., A_{N,n-1} be the n X n unit-primitive matrices (again see [Jeffery]) associated with N, and define the Chebyshev polynomials of the second kind by the recurrence U_0(x) = 1, U_1(x) = 2*x and U_r(x) = 2*x*U_(r-1)(x) - U_(r-2)(x)  (r>1). Define the column vectors V_(k-1) = (U_(k-1)(cos(Pi/N)), U_(k-1)(cos(3*Pi/N)), ..., U_(k-1)(cos((2*n-1)*Pi/N)))^T, where T denotes matrix transpose. Let S_N = [V_0, V_1, ..., V_(n-1)] be the n X n matrix formed by taking V_(k-1) as column k-1. Let X_N = [S_N]^T*S_N, and let [X_N](i,j) denote the entry in row i and column j of X_N, i,j in {0,...,n-1}. Then t(n,k) = [X_N](k-1,k-1), and row n of the triangle is given by the main diagonal entries of X_N. Remarks: Hence t(n,k) is the sum of squares t(n,k) = sum[m=1,...,n (U_(k-1)(cos((2*m-1)*Pi/N)))^2]. Finally, this sequence is related to A057059, since X_N = [sum_{m=1,...,n} A057059(n,m)*A_{N,m-1}] is also an integral linear combination of unit-primitive matrices from the N-th set. - L. Edson Jeffery, Jan 20 2012
Row sums: n*(n+1)*(2*n+1)/6. - L. Edson Jeffery, Jan 25 2013
n-th row = partial sums of n-th row of A004736. - Reinhard Zumkeller, Aug 04 2014
T(n,k) is the number of distinct sums made by at most k elements in {1, 2, ... n}, for 1 <= k <= n, e.g., T(6,2) = the number of distinct sums made by at most 2 elements in {1,2,3,4,5,6}. The sums range from 1, to 5+6=11. So there are 11 distinct sums. - Derek Orr, Nov 26 2014
A number n occurs in this sequence A001227(n) times, the number of odd divisors of n, see A209260. - Hartmut F. W. Hoft, Apr 14 2016
Conjecture: 2*n + 1 is composite if and only if gcd(t(n,m),m) != 1, for some m. - L. Edson Jeffery, Jan 30 2018
From Peter Munn, Aug 21 2019 in respect of the sequence read as a triangle: (Start)
A number m can be found in column k if and only if A286013(m, k) is nonzero, in which case m occurs in column k on row A286013(m, k).
The first occurrence of m is in row A212652(m) column A109814(m), which is the rightmost column in which m occurs. This occurrence determines where m appears in A209260. The last occurrence of m is in row m column 1.
Viewed as a sequence of rows, consider the subsequences (of rows) that contain every positive integer. The lexicographically latest of these subsequences consists of the rows with row numbers in A270877; this is the only one that contains its own row numbers only once.
(End)

			As a triangle:
   1,
   2,  3,
   3,  5,  6,
   4,  7,  9, 10,
   5,  9, 12, 14, 15,
   6, 11, 15, 18, 20, 21,
   7, 13, 18, 22, 25, 27, 28,
   8, 15, 21, 26, 30, 33, 35, 36,
   9, 17, 24, 30, 35, 39, 42, 44, 45,
  10, 19, 27, 34, 40, 45, 49, 52, 54, 55;
As a rectangle:
   1   2   3   4   5   6   7   8   9  10
   3   5   7   9  11  13  15  17  19  21
   6   9  12  15  18  21  24  27  30  33
  10  14  18  22  26  30  34  38  42  46
  15  20  25  30  35  40  45  50  55  60
  21  27  33  39  45  51  57  63  69  75
  28  35  42  49  56  63  70  77  84  91
  36  44  52  60  68  76  84  92 100 108
  45  54  63  72  81  90  99 108 117 126
  55  65  75  85  95 105 115 125 135 145
Since the odd divisors of 15 are 1, 3, 5 and 15, number 15 appears four times in the triangle at t(3+(5-1)/2, 5) in column 5 since 5+1 <= 2*3, t(5+(3-1)/2, 3), t(1+(15-1)/2, 2*1) in column 2 since 15+1 > 2*1, and t(15+(1-1)/2, 1). - _Hartmut F. W. Hoft_, Apr 14 2016

R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
Johann Cigler, Some elementary observations on Narayana polynomials and related topics, arXiv:1611.05252 [math.CO], 2016. See p. 24.
Carlton Gamer, David W. Roeder, and John J. Watkins, Trapezoidal Numbers, Mathematics Magazine 58:2 (1985), pp. 108-110.
L. E. Jeffery, Unit-primitive matrices
M. A. Nyblom, On the representation of the integers as a difference of nonconsecutive triangular numbers, Fibonacci Quarterly 39:3 (2001), pp. 256-263.

Cf. A000330 (row sums), A004736, A057059, A070543.
A144112, A051340, A141419, A185874, A185875, A185876 are accumulation chain related.
A141418 is a variant.
Cf. A001227, A209260. - Hartmut F. W. Hoft, Apr 14 2016
A109814, A212652, A270877, A286013 relate to where each natural number appears in this sequence.
A000027, A000217, A000326, A005449, A045943, A059845, A115067, A140090, A140091, A140672 are rows, columns or diagonals - refer to comments.

a141419 n k =  k * (2 * n - k + 1) `div` 2
a141419_row n = a141419_tabl !! (n-1)
a141419_tabl = map (scanl1 (+)) a004736_tabl
-- Reinhard Zumkeller, Aug 04 2014

a:=(n,k)->k*n-binomial(k,2): seq(seq(a(n,k),k=1..n),n=1..12); # Muniru A Asiru, Oct 14 2018

T[n_, m_] = m*(2*n - m + 1)/2; a = Table[Table[T[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[a]

t(n,m) = m*(2*n - m + 1)/2.
t(n,m) = A000217(n) - A000217(n-m). - L. Edson Jeffery, Jan 16 2013
Let v = d*h with h odd be an integer factorization, then v = t(d+(h-1)/2, h) if h+1 <= 2*d, and v = t(d+(h-1)/2, 2*d) if h+1 > 2*d; see A209260. - Hartmut F. W. Hoft, Apr 14 2016
G.f.: y*(-x + y)/((-1 + x)^2*(-1 + y)^3). - Stefano Spezia, Oct 14 2018
T(n, 2) = A060747(n) for n > 1. T(n, 3) = A008585(n - 1) for n > 2. T(n, 4) = A016825(n - 2) for n > 3. T(n, 5) = A008587(n - 2) for n > 4. T(n, 6) = A016945(n - 3) for n > 5. T(n, 7) = A008589(n - 3) for n > 6. T(n, 8) = A017113(n - 4) for n > 7.r n > 5. T(n, 7) = A008589(n - 3) for n > 6. T(n, 8) = A017113(n - 4) for n > 7. T(n, 9) = A008591(n - 4) for n > 8. T(n, 10) = A017329(n - 5) for n > 9. T(n, 11) = A008593(n - 5) for n > 10.  T(n, 12) = A017593(n - 6) for n > 11. T(n, 13) = A008595(n - 6) for n > 12. T(n, 14) = A147587(n - 7) for n > 13. T(n, 15) = A008597(n - 7) for n > 14. T(n, 16) = A051062(n - 8) for n > 15. T(n, 17) = A008599(n - 8) for n > 16. - Stefano Spezia, Oct 14 2018
T(2*n-k, k) = A070543(n, k). - Peter Munn, Aug 21 2019

Simpler name by Stefano Spezia, Oct 14 2018

A017053 a(n) = 7*n + 6.

Original entry on oeis.org

6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 76, 83, 90, 97, 104, 111, 118, 125, 132, 139, 146, 153, 160, 167, 174, 181, 188, 195, 202, 209, 216, 223, 230, 237, 244, 251, 258, 265, 272, 279, 286, 293, 300, 307, 314, 321, 328, 335, 342, 349, 356, 363, 370, 377, 384

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Tanya Khovanova, Recursive Sequences
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 955
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008589, A016993, A017005, A017017.

[7*n + 6: n in [0..60]]; // Vincenzo Librandi, Jun 18 2011

Array[7*#+6&,100,0] (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)
LinearRecurrence[{2,-1},{6,13},60] (* Harvey P. Dale, Apr 13 2022 *)

a(n)=7*n+6 \\ Charles R Greathouse IV, Jul 10 2016

a(n) = 2*a(n-1) - a(n-2). - Wesley Ivan Hurt, Mar 17 2023

G.f.: (6+x)/(1-x)^2. - Wesley Ivan Hurt, Dec 28 2023

A033582 a(n) = 7*n^2.

Original entry on oeis.org

0, 7, 28, 63, 112, 175, 252, 343, 448, 567, 700, 847, 1008, 1183, 1372, 1575, 1792, 2023, 2268, 2527, 2800, 3087, 3388, 3703, 4032, 4375, 4732, 5103, 5488, 5887, 6300, 6727, 7168, 7623, 8092, 8575, 9072, 9583, 10108, 10647, 11200, 11767, 12348, 12943, 13552, 14175

Offset: 0

N. J. A. Sloane

From Roberto E. Martinez II, Jan 07 2002: (Start)
Number of edges of the complete bipartite graph of order 8n, K_n,7n.
Number of edges of the complete tripartite graph of order 5n, K_n,n,3n. (End)

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000290, A008589, A132111, A195041.

7Range[0, 49]^2 (* Alonso del Arte, Jun 30 2013 *)

a(n)=7*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Central terms of the triangle in A132111: a(n) = A132111(2*n,n). - Reinhard Zumkeller, Aug 10 2007
a(n) = 7*A000290(n). - Omar E. Pol, Dec 11 2008
a(n) = 14*n + a(n-1) - 7 (with a(0) = 0). - Vincenzo Librandi, Aug 05 2010
G.f.: -7*x*(1+x)/(x-1)^3. - R. J. Mathar, Feb 06 2017
From Amiram Eldar, Feb 03 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/42.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/84.
Product_{n>=1} (1 + 1/a(n)) = sqrt(7)*sinh(Pi/sqrt(7))/Pi.
Product_{n>=1} (1 - 1/a(n)) = sqrt(7)*sin(Pi/sqrt(7))/Pi. (End)
From Elmo R. Oliveira, Dec 02 2024: (Start)
E.g.f.: 7*exp(x)*x*(1 + x).
a(n) = n*A008589(n) = A195041(2*n).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A113807 Permutation of natural numbers generated by 7-rowed array shown below.

Original entry on oeis.org

1, 13, 2, 15, 12, 3, 27, 16, 11, 4, 29, 26, 17, 10, 5, 41, 30, 25, 18, 9, 6, 43, 40, 31, 24, 19, 8, 7, 55, 44, 39, 32, 23, 20, 14, 57, 54, 45, 38, 33, 22, 21, 69, 58, 53, 46, 37, 34, 28, 71, 68, 59, 52, 47, 36, 35, 83, 72, 67, 60, 51, 48, 42, 85, 82, 73, 66, 61, 50, 49

Offset: 1

Giovanni Teofilatto, Jan 22 2006

nonn

For such arrays A_k see the k-family of 2k-periodic sequences P_k defined in a comment on A203571. There the k residue classes mod n have been defined. The present array is A_7 if the last class, starting with 7, is taken as first class [0] after adding a 0 in front. Then one obtains a permutation of the nonnegative integers. However, each complete residue class also includes its negative members. - Wolfdieter Lang, Feb 02 2012

			1 13 15 27 29 41 43 55 57 69 71 83 85 ... (A113801)
2 12 16 26 30 40 44 54 58 68 72 82 86 ... (A113802)
3 11 17 25 31 39 45 53 59 67 73 81 87 ... (A113803)
4 10 18 24 32 38 46 52 60 66 74 80 88 ... (A113804)
5  9 19 23 33 37 47 51 61 65 75 70 89 ... (A113805)
6  8 20 22 34 36 48 50 62 64 76 78 90 ... (A113806)
7 14 21 28 35 42 49 56 63 70 77 84 91 ... (A008589)

Cf. A088520, A090243, A090298, A092260, A204453.

A-numbers added for array rows by Wolfdieter Lang, Dec 15 2011

More terms from Ray Chandler, Dec 15 2011

A283078 a(n) = sigma(7*n).

Original entry on oeis.org

8, 24, 32, 56, 48, 96, 57, 120, 104, 144, 96, 224, 112, 171, 192, 248, 144, 312, 160, 336, 228, 288, 192, 480, 248, 336, 320, 399, 240, 576, 256, 504, 384, 432, 342, 728, 304, 480, 448, 720, 336, 684, 352, 672, 624, 576, 384, 992, 400, 744, 576, 784, 432, 960

Offset: 1

Seiichi Manyama, Feb 28 2017

nonn

			For n = 3, the divisors of 3*7 are {1, 3, 7, 21}. Now, 1 + 3 + 7 + 21 = 32. So, a(3) = 32. - _Indranil Ghosh_, Feb 28 2017

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Sigma(k*n): A000203 (k=1), A062731 (k=2), A144613 (k=3), A193553 (k=4), A283118 (k=5), A224613 (k=6), this sequence (k=7), A283122 (k=8), A283123 (k=9).

Cf. A008589.

Table[DivisorSigma[1,7n],{n,1,54}] (* Indranil Ghosh, Feb 28 2017 *)

a(n) = sigma(7*n) \\ Indranil Ghosh, Feb 28 2017

From Amiram Eldar, Dec 16 2022: (Start)
a(n) = A000203(7*n) = A000203(A008589(n)).
Sum_{k=1..n} a(k) = (55*Pi^2/84) * n^2 + O(n*log(n)). (End)

A008603 Multiples of 21.

Original entry on oeis.org

0, 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029, 1050, 1071, 1092

Offset: 0

N. J. A. Sloane

Sum of the numbers from 3*(n-1) to 3*(n+1). - Bruno Berselli, Oct 25 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 333.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008585, A008589, A008601, A008602.

A008603:= func< n | 21*n >; // G. C. Greubel, Apr 16 2025

Range[0, 1500, 21] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
CoefficientList[Series[21 x/(1-x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Jun 10 2013 *)

a(n)=21*n \\ Charles R Greathouse IV, Oct 07 2015

def A008603(n): return 21*n # G. C. Greubel, Apr 16 2025

G.f.: 21*x/(1-x)^2. - Vincenzo Librandi, Jun 10 2013
From Elmo R. Oliveira, Apr 08 2025: (Start)
E.g.f.: 21*x*exp(x).
a(n) = A008585(A008589(n)) = A008589(A008585(n)). (End)

cp's OEIS Frontend

A017005 a(n) = 7n + 2.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A008596 Multiples of 14.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A084968 Multiples of 7 coprime to 30.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A109720 Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Sage

Formula

A141419 Triangle read by rows: T(n, k) = A000217(n) - A000217(n - k) with 1 <= k <= n.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

Formula

Extensions

A017053 a(n) = 7*n + 6.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A033582 a(n) = 7*n^2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs