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.

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A303273 Array T(n,k) = binomial(n, 2) + k*n + 1 read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 3, 4, 4, 1, 4, 6, 7, 7, 1, 5, 8, 10, 11, 11, 1, 6, 10, 13, 15, 16, 16, 1, 7, 12, 16, 19, 21, 22, 22, 1, 8, 14, 19, 23, 26, 28, 29, 29, 1, 9, 16, 22, 27, 31, 34, 36, 37, 37, 1, 10, 18, 25, 31, 36, 40, 43, 45, 46, 46, 1, 11, 20, 28, 35, 41
Offset: 0

Views

Author

Franck Maminirina Ramaharo, Apr 20 2018

Keywords

Comments

Columns are linear recurrence sequences with signature (3,-3,1).
8*T(n,k) + A166147(k-1) are squares.
Columns k are binomial transforms of [1, k, 1, 0, 0, 0, ...].
Antidiagonals sums yield A116731.

Examples

			The array T(n,k) begins
1    1    1    1    1    1    1    1    1    1    1    1    1  ...  A000012
1    2    3    4    5    6    7    8    9   10   11   12   13  ...  A000027
2    4    6    8   10   12   14   16   18   20   22   24   26  ...  A005843
4    7   10   13   16   19   22   25   28   31   34   37   40  ...  A016777
7   11   15   19   23   27   31   35   39   43   47   51   55  ...  A004767
11  16   21   26   31   36   41   46   51   56   61   66   71  ...  A016861
16  22   28   34   40   46   52   58   64   70   76   82   88  ...  A016957
22  29   36   43   50   57   64   71   78   85   92   99  106  ...  A016993
29  37   45   53   61   69   77   85   93  101  109  117  125  ...  A004770
37  46   55   64   73   82   91  100  109  118  127  136  145  ...  A017173
46  56   66   76   86   96  106  116  126  136  146  156  166  ...  A017341
56  67   78   89  100  111  122  133  144  155  166  177  188  ...  A017401
67  79   91  103  115  127  139  151  163  175  187  199  211  ...  A017605
79  92  105  118  131  144  157  170  183  196  209  222  235  ...  A190991
...
The inverse binomial transforms of the columns are
1    1    1    1    1    1    1    1    1    1    1    1    1  ...
0    1    2    3    4    5    6    7    8    9   10   11   12  ...
1    1    1    1    1    1    1    1    1    1    1    1    1  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
...
T(k,n-k) = A087401(n,k) + 1 as triangle
1
1   1
1   2   2
1   3   4   4
1   4   6   7   7
1   5   8  10  11  11
1   6  10  13  15  16  16
1   7  12  16  19  21  22  22
1   8  14  19  23  26  28  29  29
1   9  16  22  27  31  34  36  37  37
1  10  18  25  31  36  40  43  45  46  46
...

References

  • R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, 1994.

Crossrefs

Cf. A085475, A086270, A086271, A086272, A086273, A130154, A159798, A162609, A162610, A300401.

Programs

  • Maple
    T := (n, k) -> binomial(n, 2) + k*n + 1;
for n from 0 to 20 do seq(T(n, k), k = 0 .. 20) od;
  • Mathematica
    Table[With[{n = m - k}, Binomial[n, 2] + k n + 1], {m, 0, 11}, {k, m, 0, -1}] // Flatten (* Michael De Vlieger, Apr 21 2018 *)
  • Maxima
    T(n, k) := binomial(n, 2)+ k*n + 1$
for n:0 thru 20 do
    print(makelist(T(n, k), k, 0, 20));
  • PARI
    T(n,k) = binomial(n, 2) + k*n + 1;
tabl(nn) = for (n=0, nn, for (k=0, nn, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 17 2018

Formula

G.f.: (3*x^2*y - 3*x*y + y - 2*x^2 + 2*x - 1)/((x - 1)^3*(y - 1)^2).
E.g.f.: (1/2)*(2*x*y + x^2 + 2)*exp(y + x).
T(n,k) = 3*T(n-1,k) - 3*T(n-2,k) + T(n-3,k), with T(0,k) = 1, T(1,k) = k + 1 and T(2,k) = 2*k + 2.
T(n,k) = T(n-1,k) + n + k - 1.
T(n,k) = T(n,k-1) + n, with T(n,0) = 1.
T(n,0) = A152947(n+1).
T(n,1) = A000124(n).
T(n,2) = A000217(n).
T(n,3) = A034856(n+1).
T(n,4) = A052905(n).
T(n,5) = A051936(n+4).
T(n,6) = A246172(n+1).
T(n,7) = A302537(n).
T(n,8) = A056121(n+1) + 1.
T(n,9) = A056126(n+1) + 1.
T(n,10) = A051942(n+10) + 1, n > 0.
T(n,11) = A101859(n) + 1.
T(n,12) = A132754(n+1) + 1.
T(n,13) = A132755(n+1) + 1.
T(n,14) = A132756(n+1) + 1.
T(n,15) = A132757(n+1) + 1.
T(n,16) = A132758(n+1) + 1.
T(n,17) = A212427(n+1) + 1.
T(n,18) = A212428(n+1) + 1.
T(n,n) = A143689(n) = A300192(n,2).
T(n,n+1) = A104249(n).
T(n,n+2) = T(n+1,n) = A005448(n+1).
T(n,n+3) = A000326(n+1).
T(n,n+4) = A095794(n+1).
T(n,n+5) = A133694(n+1).
T(n+2,n) = A005449(n+1).
T(n+3,n) = A115067(n+2).
T(n+4,n) = A133694(n+2).
T(2*n,n) = A054556(n+1).
T(2*n,n+1) = A054567(n+1).
T(2*n,n+2) = A033951(n).
T(2*n,n+3) = A001107(n+1).
T(2*n,n+4) = A186353(4*n+1) (conjectured).
T(2*n,n+5) = A184103(8*n+1) (conjectured).
T(2*n,n+6) = A250657(n-1) = A250656(3,n-1), n > 1.
T(n,2*n) = A140066(n+1).
T(n+1,2*n) = A005891(n).
T(n+2,2*n) = A249013(5*n+4) (conjectured).
T(n+3,2*n) = A186384(5*n+3) = A186386(5*n+3) (conjectured).
T(2*n,2*n) = A143689(2*n).
T(2*n+1,2*n+1) = A143689(2*n+1) (= A030503(3*n+3) (conjectured)).
T(2*n,2*n+1) = A104249(2*n) = A093918(2*n+2) = A131355(4*n+1) (= A030503(3*n+5) (conjectured)).
T(2*n+1,2*n) = A085473(n).
a(n+1,5*n+1)=A051865(n+1) + 1.
a(n,2*n+1) = A116668(n).
a(2*n+1,n) = A054569(n+1).
T(3*n,n) = A025742(3*n-1), n > 1 (conjectured).
T(n,3*n) = A140063(n+1).
T(n+1,3*n) = A069099(n+1).
T(n,4*n) = A276819(n).
T(4*n,n) = A154106(n-1), n > 0.
T(2^n,2) = A028401(n+2).
T(1,n)*T(n,1) = A006000(n).
T(n*(n+1),n) = A211905(n+1), n > 0 (conjectured).
T(n*(n+1)+1,n) = A294259(n+1).
T(n,n^2+1) = A081423(n).
T(n,A000217(n)) = A158842(n), n > 0.
T(n,A152947(n+1)) = A060354(n+1).
floor(T(n,n/2)) = A267682(n) (conjectured).
floor(T(n,n/3)) = A025742(n-1), n > 0 (conjectured).
floor(T(n,n/4)) = A263807(n-1), n > 0 (conjectured).
ceiling(T(n,2^n)/n) = A134522(n), n > 0 (conjectured).
ceiling(T(n,n/2+n)/n) = A051755(n+1) (conjectured).
floor(T(n,n)/n) = A133223(n), n > 0 (conjectured).
ceiling(T(n,n)/n) = A007494(n), n > 0.
ceiling(T(n,n^2)/n) = A171769(n), n > 0.
ceiling(T(2*n,n^2)/n) = A046092(n), n > 0.
ceiling(T(2*n,2^n)/n) = A131520(n+2), n > 0.

A329523 a(n) = n * (binomial(n + 1, 3) + 1).

Original entry on oeis.org

0, 1, 4, 15, 44, 105, 216, 399, 680, 1089, 1660, 2431, 3444, 4745, 6384, 8415, 10896, 13889, 17460, 21679, 26620, 32361, 38984, 46575, 55224, 65025, 76076, 88479, 102340, 117769, 134880, 153791, 174624, 197505, 222564, 249935, 279756, 312169, 347320, 385359, 426440
Offset: 0

Views

Author

Ilya Gutkovskiy, Nov 15 2019

Keywords

Comments

The n-th centered n-gonal pyramidal number.

Examples

			Square array begins:
  (0), 1,  2,   3,   4,    5,  ... A001477
   0, (1), 3,   7,  14,   25,  ... A004006
   0,  1, (4), 11,  24,   45,  ... A006527
   0,  1,  5, (15), 34,   65,  ... A006003 (partial sums of A005448)
   0,  1,  6,  19, (44),  85,  ... A005900 (partial sums of A001844)
   0,  1,  7,  23,  54, (105), ... A004068 (partial sums of A005891)
...
This sequence is the main diagonal of the array.

References

  • E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), 142.

Links

Crossrefs

Cf. A000292, A000330, A002415, A002417, A006000, A006484, A008911, A050407, A060354, A100119, A188475 (first differences).

Programs

  • Magma
    [ n*(Binomial(n+1,3)+1):n in [0..40]]; // Marius A. Burtea, Nov 15 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 41); [0] cat Coefficients(R!(x*(1-x+5*x^2-x^3)/(1-x)^5)); // Marius A. Burtea, Nov 15 2019
  • Mathematica
    Table[n (Binomial[n + 1, 3] + 1), {n, 0, 40}]
nmax = 40; CoefficientList[Series[x (1 - x + 5 x^2 - x^3)/(1 - x)^5, {x, 0, nmax}], x]
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 4, 15, 44}, 41]

Formula

G.f.: x * (1 - x + 5*x^2 - x^3) / (1 - x)^5.
E.g.f.: exp(x) * x * (1 + x + x^2 + x^3 / 6).
a(n) = n * (n + 2) * (n^2 - 2*n + 3) / 6.
a(n) = n * (A000292(n-1) + 1).
a(n) = n + 2 * Sum_{k=1..n} A000330(k-1).
a(n) + a(-n) = 4 * A002415(n).

A349935 Array read by ascending antidiagonals: A(n, k) is the n-th spin s-Catalan number, with s = k/2.

Original entry on oeis.org

1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 5, 6, 4, 1, 1, 0, 15, 0, 5, 0, 1, 14, 36, 34, 16, 6, 1, 1, 0, 91, 0, 65, 0, 7, 0, 1, 42, 232, 364, 260, 111, 31, 8, 1, 1, 0, 603, 0, 1085, 0, 175, 0, 9, 0, 1, 132, 1585, 4269, 4600, 2666, 981, 260, 51, 10, 1, 1, 0, 4213, 0, 19845, 0, 5719, 0, 369, 0, 11, 0, 1
Offset: 1

Views

Author

Stefano Spezia, Dec 06 2021

Keywords

Examples

			The array begins:
n\k | 1    2    3    4    5    6
----+---------------------------
  1 | 1    1    1    1    1    1 ...
  2 | 0    1    0    1    0    1 ...
  3 | 2    3    4    5    6    7 ...
  4 | 0    6    0   16    0   31 ...
  5 | 5   15   34   65  111  175 ...
  6 | 0   36    0  260    0  981 ...
  ...

Links

Crossrefs

Cf. A000012 (1st row), A059841 (2nd row).
Cf. A000027, A005043, A005891, A006003, A126120.
Cf. A349934.

Programs

  • Mathematica
    T[n_,k_,s_]:=If[k==0,1,Coefficient[(Sum[x^i,{i,0,s}])^n,x^k]]; A[n_,k_]:=T[n,k(n+1)/2,k]-T[n,k(n+1)/2+1,k]; Flatten[Table[A[n-k+1,k],{n,12},{k,n}]]

Formula

A(n, k) = T(n, k*(n+1)/2, k) - T(n, k*(n+1)/2+1, k), where T(n, k, s) is the s-binomial coefficient defined as the coefficient of x^k in (Sum_{i=0..s} x^i)^n.
A(n, 1) = A126120(n+1).
A(n, 2) = A005043(n+1).
A(3, n) = A000027(n+1).
A(4, 2*n) = A005891(n).
A(5, n) = A006003(n+1).

A355010 Array read by ascending antidiagonals: T(n, k) is the number of n-core partitions with k corners.

Original entry on oeis.org

1, 3, 1, 6, 5, 1, 10, 16, 7, 1, 15, 40, 31, 9, 1, 21, 85, 105, 51, 11, 1, 28, 161, 295, 219, 76, 13, 1, 36, 280, 721, 771, 396, 106, 15, 1, 45, 456, 1582, 2331, 1681, 650, 141, 17, 1, 55, 705, 3186, 6244, 6083, 3235, 995, 181, 19, 1, 66, 1045, 5985, 15156, 19348, 13663, 5685, 1445, 226, 21, 1
Offset: 2

Views

Author

Stefano Spezia, Jun 15 2022

Keywords

Comments

T(n, k) is also equal to the number of cornerless Motzkin paths of length 2*k + n - 1 with n - 1 flat steps (see Theorem 3.3 and Proposition 3.4 at pp. 13 - 14 in Cho et al.).
In proposition 3.4 in Cho et al., the Narayana number is defined as N(k, i) = binomial(k, i)*binomial(k, i-1)/k, unlike A001263.

Examples

			The array begins:
    1,  1,   1,   1,    1,    1,    1,    1, ...
    3,  5,   7,   9,   11,   13,   15,   17, ...
    6, 16,  31,  51,   76,  106,  141,  181, ...
   10, 40, 105, 219,  396,  650,  995, 1445, ...
   15, 85, 295, 771, 1681, 3235, 5685, 9325, ...
   ...

Links

Crossrefs

Cf. A000012 (n = 2), A001263, A005408 (n = 3), A005891 (n = 4), A006007, A063490 (n = 5), A160747 (n = 6), A161680 (k = 1), A355011.

Programs

  • Mathematica
    T[n_,k_]:=Sum[Binomial[k,i]Binomial[k,i-1]Binomial[n+2(k-i),2k]/k,{i,Min[k,Floor[n/2]]}]; Flatten[Table[T[n-k+1,k],{n,2,12},{k,1,n-1}]]

Formula

T(n, k) = Sum_{i=1..min(k,floor(n/2))} N(k, i)*binomial(n+2*(k-i), 2*k), where N(k, i) = binomial(k, i)*binomial(k, i-1)/k. (See proposition 3.4 in Cho et al.).
T(n, 2) = A006007(n-1).

A382132 Centered pentagonal numbers which are semiprimes.

Original entry on oeis.org

6, 51, 106, 141, 226, 391, 526, 681, 766, 951, 1501, 1891, 2031, 2326, 2481, 2641, 3151, 3901, 4101, 4306, 6631, 6891, 7981, 8266, 8851, 10081, 10401, 11391, 13141, 14631, 15406, 16201, 20931, 22801, 23281, 24751, 27301, 27826, 28891, 29431, 30526, 32206, 33351, 35701, 36301, 38131, 38751
Offset: 1

Views

Author

Massimo Kofler, Mar 17 2025

Keywords

Examples

			A005891(1) = 6 = (5*1^2 + 5*1 + 2)/2 = 2*3.
A005891(4) = 51 = (5*4^2 + 5*4 + 2)/2 = 3*17.
A005891(6) = 106 = (5*6^2 + 5*6 + 2)/2 = 2*53.

Crossrefs

Intersection of A001358 and A005891.
Cf. A364610.

Programs

  • Mathematica
    Select[Table[(5*n^2 + 5*n + 2)/2, {n, 1, 125}], PrimeOmega[#] == 2 &] (* Amiram Eldar, Mar 17 2025 *)

A382696 Centered pentagonal numbers that are abundant.

Original entry on oeis.org

276, 456, 1266, 1626, 2176, 2976, 3516, 5406, 6126, 8556, 9456, 12426, 13506, 17016, 18276, 22326, 23766, 28356, 29976, 35106, 36906, 39376, 42576, 44556, 50766, 52926, 59676, 62016, 69306, 71826, 79656, 82356, 89776, 90726, 93606, 94576, 102516, 105576, 115026, 118266, 128256, 131676, 142206, 145806
Offset: 1

Views

Author

Massimo Kofler, Apr 03 2025

Keywords

Comments

The sequence is infinite, e.g. A005891(n) is a term when 1 < n == 1 or 10 (mod 12). - Robert Israel, Apr 06 2025

Examples

			276 = 2^2*3*23 is a term since it is a centered pentagonal number and less than the sum of its proper divisors (1+2+3+4+6+12+23+46+69+92+138=396).
456 = 2^3*3*19 is a term since it is a centered pentagonal number and less than the sum of its proper divisors  (1+2+3+4+6+8+12+19+24+38+ 57+ 76+114+152+228=744).

Crossrefs

Intersection of A005891 and A005101.
Cf. A379264.

Programs

  • Maple
    select(t -> numtheory:-sigma(t) > 2*t, [seq((5*n^2+5*n+2)/2, n=1..500)]); # Robert Israel, Apr 06 2025
  • Mathematica
    Select[Table[(5*n^2 + 5*n + 2)/2, {n, 1, 250}], DivisorSigma[-1, #] > 2 &] (* Amiram Eldar, Apr 03 2025 *)

A383025 Centered pentagonal numbers that are deficient.

Original entry on oeis.org

1, 16, 31, 51, 76, 106, 141, 181, 226, 331, 391, 526, 601, 681, 766, 856, 951, 1051, 1156, 1381, 1501, 1756, 1891, 2031, 2326, 2481, 2641, 2806, 3151, 3331, 3706, 3901, 4101, 4306, 4516, 4731, 4951, 5176, 5641, 5881, 6376, 6631, 6891, 7156, 7426, 7701, 7981, 8266, 8851, 9151, 9766, 10081, 10401
Offset: 1

Views

Author

Massimo Kofler, Apr 13 2025

Keywords

Comments

The centered pentagonal numbers that are prime are terms (see A145838).

Examples

			16 = 2^4 is a term since it is the 3rd centered pentagonal number and larger than the sum of its proper divisors (1+2+4+8=15).
51 = 3*17 is a term since it is the 5th centered pentagonal number and larger than the sum of its proper divisors (1+3+17=21).
76 = 2^2*19 is a term since it is the 6th centered pentagonal number and larger than the sum of its proper divisors (1+2+4+19+38=64).

Links

Crossrefs

Intersection of A005891 and A005100.
Cf. A145838, A381488, A382696.

Programs

  • Maple
    select(t -> numtheory:-sigma(t) < 2*t, [seq( (5*n^2+5*n+2)/2, n=0..100)]); # Robert Israel, May 13 2025
  • Mathematica
    Select[Table[(5*n^2 + 5*n + 2)/2, {n, 0, 65}], DivisorSigma[-1, #] < 2 &] (* Amiram Eldar, Apr 13 2025 *)

Formula

a(n) == 1 (mod 5).

A330133 a(n) = (1/16)*(5 + (-1)^(1+n) - 4*cos(n*Pi/2) + 10*n^2).

Original entry on oeis.org

0, 1, 3, 6, 10, 16, 23, 31, 40, 51, 63, 76, 90, 106, 123, 141, 160, 181, 203, 226, 250, 276, 303, 331, 360, 391, 423, 456, 490, 526, 563, 601, 640, 681, 723, 766, 810, 856, 903, 951, 1000, 1051, 1103, 1156, 1210, 1266, 1323, 1381, 1440, 1501, 1563, 1626, 1690, 1756
Offset: 0

Views

Author

Stefano Spezia, Dec 02 2019

Keywords

Comments

For n > 0, partial sums of A047201.

Links

Crossrefs

Cf. A005891, A033583 (10*n^2), A047201.

Programs

  • Magma
    I:=[0, 1, 3, 6, 10, 16]; [n le 6 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-4)-2*Self(n-5)+Self(n-6): n in [1..54]];
  • Maple
    gf:=(1/16)*(-exp(-x) + 5*exp(x)*(1 + 2*x + 2*x^2) - 4*cos(x)); ser := series(gf, x, 54):
seq(factorial(n)*coeff(ser, x, n), n = 0 .. 53)
  • Mathematica
    Table[(1/16)*(5+(-1)^(1+n)-4*Cos[n*Pi/2]+10*n^2),{n,0,53}]
LinearRecurrence[{2,-1,0,1,-2,1},{0,1,3,6,10,16},60] (* Harvey P. Dale, Jul 21 2021 *)
  • PARI
    concat([0], Vec(-x*(1 + x + x^2 + x^3 + x^4)/((-1 + x)^3*(1 + x)*(1 + x^2))+O(x^54)))

Formula

O.g.f.: -x*(1 + x + x^2 + x^3 + x^4)/((-1 + x)^3*(1 + x)*(1 + x^2)).
E.g.f.: (1/16)*(-exp(-x) + 5*exp(x)*(1 + 2*x + x^2) - 4*cos(x)).
a(n) = 2*a(n-1) - a(n-2) + a(n-4) -2*a(n-5) + a(n-6) for n > 5.
a(2*n-1) = A005891(n-1) for n > 0.
a(4*n) = 10*n^2. - Bernard Schott, Dec 06 2019

A381043 Centered pentagonal numbers which are squarefree semiprimes.

Original entry on oeis.org

6, 51, 106, 141, 226, 391, 526, 681, 766, 951, 1501, 1891, 2031, 2326, 2481, 2641, 3151, 3901, 4101, 4306, 6631, 6891, 7981, 8266, 8851, 10081, 10401, 11391, 13141, 14631, 15406, 16201, 20931, 23281, 24751, 27301, 27826, 28891, 29431, 30526, 32206, 33351, 35701, 36301, 38131, 38751, 41926
Offset: 1

Views

Author

Massimo Kofler, Apr 14 2025

Keywords

Comments

Numbers such as 22801=151^2 and 1666681=1291^2 are in A382132 but not here.

Examples

			A005891(1) = 6 = (5*1^2 + 5*1 + 2)/2 = 2*3.
A005891(4) = 51 = (5*4^2 + 5*4 + 2)/2 = 3*17.
A005891(6) = 106 = (5*6^2 + 5*6 + 2)/2 = 2*53.

Crossrefs

Intersection of A006881 and A005891.
Cf. A145838, A382132, A364610.

Programs

  • Mathematica
    Select[Table[5*n*(n + 1)/2 + 1, {n, 0, 150}], FactorInteger[#][[;; , 2]] == {1, 1} &] (* Amiram Eldar, Apr 14 2025 *)

A382451 Centered pentagonal numbers which are the products of four distinct primes.

Original entry on oeis.org

5406, 12426, 20026, 23766, 40641, 55131, 83266, 115026, 118266, 136306, 142206, 145806, 176226, 184281, 205206, 209526, 245706, 279726, 284766, 315951, 326706, 371526, 387106, 407031, 413106, 419226, 425391, 498406, 505126, 553426, 623751, 638826, 672106, 685131
Offset: 1

Views

Author

Massimo Kofler, Mar 26 2025

Keywords

Examples

			A005891(46) = 5406 = (5*46^2 + 5*46 + 2)/2 = 2*3*17*53.
A005891(70) = 12426 = (5*70^2 + 5*70 + 2)/2 = 2*3*19*109.
A005891(127) = 40641 = (5*127^2 + 5*127 + 2)/2 = 3*19*23*31.

Crossrefs

Intersection of A005891 and A046386.
Cf. A364610.

Programs

  • Mathematica
    Select[Table[5*n*(n+1)/2+1, {n, 0, 600}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &] (* Amiram Eldar, Mar 26 2025 *)
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