A028566 -id:A028566 - cp's OEIS frontend

A098832 Square array read by antidiagonals: even-numbered rows of the table are of the form n(n+m) and odd-numbered rows are of the form n(n+m)/2.

1, 3, 3, 6, 8, 2, 10, 15, 5, 5, 15, 24, 9, 12, 3, 21, 35, 14, 21, 7, 7, 28, 48, 20, 32, 12, 16, 4, 36, 63, 27, 45, 18, 27, 9, 9, 45, 80, 35, 60, 25, 40, 15, 20, 5, 55, 99, 44, 77, 33, 55, 22, 33, 11, 11, 66, 120, 54, 96, 42, 72, 30, 48, 18, 24, 6, 78, 143, 65, 117, 52, 91, 39, 65, 26, 39, 13, 13

Offset: 1

Eugene McDonnell (eemcd(AT)mac.com), Nov 02 2004

The rows of this table and that in A098737 are related. Given a function f = n/( 1 + (1+n) mod(2) ), row n of A098737 can be derived from row n of T by multiplying the latter by f(n); row n of T can be derived from row n of A098737 by dividing the latter by f(n).

			Array begins as:
  1,  3,  6, 10, 15, 21,  28,  36,  45 ... A000217;
  3,  8, 15, 24, 35, 48,  63,  80,  99 ... A005563;
  2,  5,  9, 14, 20, 27,  35,  44,  54 ... A000096;
  5, 12, 21, 32, 45, 60,  77,  96, 117 ... A028347;
  3,  7, 12, 18, 25, 33,  42,  52,  63 ... A027379;
  7, 16, 27, 40, 55, 72,  91, 112, 135 ... A028560;
  4,  9, 15, 22, 30, 39,  49,  60,  72 ... A055999;
  9, 20, 33, 48, 65, 84, 105, 128, 153 ... A028566;
  5, 11, 18, 26, 35, 45,  56,  68,  81 ... A056000;
Antidiagonals begin as:
   1;
   3,  3;
   6,  8,  2;
  10, 15,  5,  5;
  15, 24,  9, 12,  3;
  21, 35, 14, 21,  7,  7;
  28, 48, 20, 32, 12, 16,  4;
  36, 63, 27, 45, 18, 27,  9,  9;
  45, 80, 35, 60, 25, 40, 15, 20,  5;
  55, 99, 44, 77, 33, 55, 22, 33, 11, 11;

G. C. Greubel, Antidiagonals n = 1..50, flattened

Row m of array: A000217 (m=1), A005563 (m=2), A000096 (m=3), A028347 (m=4), A027379 (m=5), A028560 (m=6), A055999 (m=7), A028566 (m=8), A056000 (m=9), A098603 (m=10), A056115 (m=11), A098847 (m=12), A056119 (m=13), A098848 (m=14), A056121 (m=15), A098849 (m=16), A056126 (m=17), A098850 (m=18), A051942 (m=19).
Column m of array: A026741 (m=1), A022998 (m=2), A165351 (m=3).
Cf. A098737, A168509, A181900.

A098832:= func< n,k | (1/4)*(3+(-1)^k)*(n+1)*(n-k+1) >;
[A098832(n,k): k in [1..n], n in [1..15]]; // G. C. Greubel, Jul 31 2022

A098832[n_, k_]:= (1/4)*(3+(-1)^k)*(n+1)*(n-k+1);
Table[A098832[n,k], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Jul 31 2022 *)

def A098832(n,k): return (1/4)*(3+(-1)^k)*(n+1)*(n-k+1)
flatten([[A098832(n,k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Jul 31 2022

Item m of row n of T is given (in infix form) by: n T m = n * (n + m) / (1 + m (mod 2)). E.g. Item 4 of row 3 of T: 3 T 4 = 14.
From G. C. Greubel, Jul 31 2022: (Start)
A(n, k) = (1/4)*(3 + (-1)^n)*k*(k+n) (array).
T(n, k) = (1/4)*(3 + (-1)^k)*(n+1)*(n-k+1) (antidiagonal triangle).
Sum_{k=1..n} T(n, k) = (1/8)*(n+1)*( (3*n-1)*(n+1) + (1+(-1)^n)/2 ).
T(2*n-1, n) = A181900(n).
T(2*n+1, n) = 2*A168509(n+1). (End)

Missing terms added by G. C. Greubel, Jul 31 2022

A132768 a(n) = n*(n + 26).

Original entry on oeis.org

0, 27, 56, 87, 120, 155, 192, 231, 272, 315, 360, 407, 456, 507, 560, 615, 672, 731, 792, 855, 920, 987, 1056, 1127, 1200, 1275, 1352, 1431, 1512, 1595, 1680, 1767, 1856, 1947, 2040, 2135, 2232, 2331, 2432, 2535, 2640, 2747, 2856, 2967, 3080, 3195, 3312, 3431

Offset: 0

Omar E. Pol, Aug 28 2007

G. C. Greubel, Table of n, a(n) for n = 0..5000
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
Cf. A098849, A098850, A098603, A098847, A098848, A102928, A120071, A132759, A132760, A132761.
Cf. A132762, A132763, A132764, A132765, A132766, A132767.

Table[n(n+26),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,27,56},50] (* Harvey P. Dale, Dec 15 2018 *)

a(n)=n*(n+26) \\ Charles R Greathouse IV, Jun 17 2017

[n*(n+26) for n in (0..50)] # G. C. Greubel, Mar 13 2022

a(n) = n*(n + 26).
a(n) = 2*n + a(n-1) + 25, with a(0)=0. - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(26)/26 = A001008(26)/A102928(26) = 34395742267/232016584800, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 18051406831/696049754400. (End)
From G. C. Greubel, Mar 13 2022: (Start)
G.f.: x*(27 - 25*x)/(1-x)^3.
E.g.f.: x*(27 + x)*exp(x). (End)

A225948 a(0) = -1; for n>0, a(n) = numerator(1/4 - 4/n^2).

Original entry on oeis.org

-1, -15, -3, -7, 0, 9, 5, 33, 3, 65, 21, 105, 2, 153, 45, 209, 15, 273, 77, 345, 6, 425, 117, 513, 35, 609, 165, 713, 12, 825, 221, 945, 63, 1073, 285, 1209, 20, 1353, 357, 1505, 99, 1665, 437, 1833, 30, 2009, 525, 2193, 143

Offset: 0

Paul Curtz, May 21 2013

Denominators are in A226008.
Fractions in lowest terms for n>0: -15/4, -3/4, -7/36, 0/1, 9/100, 5/36, 33/196, 3/16, 65/324, 21/100, 105/484, 2/9, 153/676, 45/196, 209/900, 15/64,...
If t(n) is the sequence with period 8: 4, 64, 16, 64, 1, 64, 16, 64, 4, 64, 16, ... (see A226044), then A226008(n) = 4*a(n) + t(n).

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,1).

Cf. A000466, A028566, A061037, A061041, A078371, A106609, A142705, A145923, A226008.

[-1] cat [Numerator(1/4-4/n^2): n in [1..50]]; // Bruno Berselli, May 22 2013

Join[{-1}, Table[Numerator[1/4 - 4/n^2], {n, 50}]] (* Bruno Berselli, May 24 2013 *)

concat([-1], vector(100, n, numerator(1/4 - 4/n^2))) \\ G. C. Greubel, Sep 19 2018

a(n) = 3*a(n-8) -3*a(n-16) +a(n-24).
a(2n) = A061037(n), a(2n+1) = A145923(n-2) for A145923(-2)=-15, A145923(-1)=-7.
a(4n)   = A142705(n) for A142705(0)=-1, a(8n) = A000466(n);
a(4n+1) = A028566(4n-3) for A028566(-3)=-15;
a(4n+2) = A078371(n-1) for A078371(-1)=-3;
a(4n+3) = A028566(4n-1) for A028566(-1)=-7.
a(n+4)  = A106609(n) * A106609(n+8).
G.f.: -(1 +15*x +3*x^2 +7*x^3 -9*x^5 -5*x^6 -33*x^7 -6*x^8 -110*x^9 -30*x^10 -126*x^11 -2*x^12 -126*x^13 -30*x^14 -110*x^15 -3*x^16 -33*x^17 -5*x^18 -9*x^19 +7*x^21 +3*x^22 +15*x^23)/(1-x^8)^3. - Bruno Berselli, May 22 2013
a(n) = (n^2-16)*(6*cos(Pi*n/4)-54*cos(Pi*n/2)+6*cos(3*Pi*n/4)-219*(-1)^n+293)/512. - Bruno Berselli, May 22 2013
a(n+10) = a(n+2)*(n+14)/(n-2) for n=0,1 and n>2. - Bruno Berselli, May 22 2013

Edited by Bruno Berselli, May 22 2013

A132769 a(n) = n*(n + 27).

Original entry on oeis.org

0, 28, 58, 90, 124, 160, 198, 238, 280, 324, 370, 418, 468, 520, 574, 630, 688, 748, 810, 874, 940, 1008, 1078, 1150, 1224, 1300, 1378, 1458, 1540, 1624, 1710, 1798, 1888, 1980, 2074, 2170, 2268, 2368, 2470, 2574, 2680, 2788, 2898, 3010, 3124, 3240, 3358, 3478

Offset: 0

Omar E. Pol, Aug 28 2007

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566.
Cf. A028569, A098849, A098850, A098603, A098847, A098848, A102928, A120071, A132759.
Cf. A132760, A132761, A132762, A132763, A132764, A132765, A132766, A132767, A132768.
Cf. A132756.

Table[n(n+27),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,28,58},50] (* Harvey P. Dale, Oct 14 2012 *)

a(n)=n*(n+27) \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 2*n + a(n-1) + 26, with a(0)=0. - Vincenzo Librandi, Aug 03 2010
a(0)=0, a(1)=28, a(2)=58; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Oct 14 2012
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(27)/27 = A001008(27)/A102928(27) = 312536252003/2168462696400, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/27 - 57128792093/2168462696400. (End)
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: 2*x*(14 - 13*x)/(1 - x)^3.
E.g.f.: exp(x)*x*(28 + x).
a(n) = 2*A132756(n). (End)

A105020 Array read by antidiagonals: row n (n >= 0) contains the numbers m^2 - n^2, m >= n+1.

Original entry on oeis.org

1, 3, 4, 5, 8, 9, 7, 12, 15, 16, 9, 16, 21, 24, 25, 11, 20, 27, 32, 35, 36, 13, 24, 33, 40, 45, 48, 49, 15, 28, 39, 48, 55, 60, 63, 64, 17, 32, 45, 56, 65, 72, 77, 80, 81, 19, 36, 51, 64, 75, 84, 91, 96, 99, 100, 21, 40, 57, 72, 85, 96, 105, 112, 117, 120, 121

Offset: 0

Andrew S. Plewe and Franklin T. Adams-Watters, Jul 11 2005

A "Goldbach Conjecture" for this sequence: when there are n terms between consecutive odd integers (2n+1) and (2n+3) for n > 0, at least one will be the product of 2 primes (not necessarily distinct). Example: n=3 for consecutive odd integers a(7)=7 and a(11)=9 and of the 3 sequence entries a(8)=12, a(9)=15 and a(10)=16 between them, one is the product of 2 primes a(9)=15=3*5. - Michael Hiebl, Jul 15 2007
A024352 gives distinct values in the array, minus the first row (1, 4, 9, 16, etc.). a(n) gives all solutions to the equation x^2 + xy = n, with y mod 2 = 0, x > 0, y >= 0. - Andrew S. Plewe, Oct 19 2007
Alternatively, triangular sequence of coefficients of Dynkin diagram weights for the Cartan groups C_n: t(n,m) = m*(2*n - m). Row sums are A002412. - Roger L. Bagula, Aug 05 2008

			Array begins:
  1  4  9 16 25 36  49  64  81 100 ...
  3  8 15 24 35 48  63  80  99 120 ...
  5 12 21 32 45 60  77  96 117 140 ...
  7 16 27 40 55 72  91 112 135 160 ...
  9 20 33 48 65 84 105 128 153 180 ...
  ...
Triangle begins:
   1;
   3,  4;
   5,  8,  9;
   7, 12, 15, 16;
   9, 16, 21, 24, 25;
  11, 20, 27, 32, 35, 36;
  13, 24, 33, 40, 45, 48, 49;
  15, 28, 39, 48, 55, 60, 63, 64;
  17, 32, 45, 56, 65, 72, 77, 80, 81;
  19, 36, 51, 64, 75, 84, 91, 96, 99, 100;

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

G. C. Greubel, Antidiagonals n = 0..50, flattened

Rows give A000290, A005563, A028347, A028560, A028566, A098603, A098847, A098848, A098849, A098850.
Columns give A005408, A008586, A016945, A008590, A017329, A008594, A008598, A008602, A008606, A000567.
Diagonals give A033428, A045944, A067725.
Cf. A000384, A002412, A024352, A105020, A128076.

[(k+1)*(2*n-k+1): k in [0..n], n in [0..15]]; // G. C. Greubel, Mar 15 2023

t[n_, m_]:= (n^2 - m^2); Flatten[Table[t[i, j], {i,12}, {j,i-1,0,-1}]]
(* to view table *) Table[t[i, j], {j,0,6}, {i,j+1,10}]//TableForm (* Robert G. Wilson v, Jul 11 2005 *)
Table[(k+1)*(2*n-k+1), {n,0,15}, {k,0,n}]//Flatten (* Roger L. Bagula, Aug 05 2008 *)

def A105020(n,k): return (k+1)*(2*n-k+1)
flatten([[A105020(n,k) for k in range(n+1)] for n in range(16)]) # G. C. Greubel, Mar 15 2023

a(n) = r^2 - (r^2 + r - m)^2/4, where r = round(sqrt(m)) and m = 2*n+2. - Wesley Ivan Hurt, Sep 04 2021
a(n) = A128076(n+1) * A105020(n+1). - Wesley Ivan Hurt, Jan 07 2022
From G. C. Greubel, Mar 15 2023: (Start)
Sum_{k=0..n} T(n, k) = A002412(n+1).
Sum_{k=0..n} (-1)^k*T(n, k) = (1/2)*((1+(-1)^n)*A000384((n+2)/2) - (1- (-1)^n)*A000384((n+1)/2)). (End)

More terms from Robert G. Wilson v, Jul 11 2005

A132770 a(n) = n*(n + 28).

Original entry on oeis.org

0, 29, 60, 93, 128, 165, 204, 245, 288, 333, 380, 429, 480, 533, 588, 645, 704, 765, 828, 893, 960, 1029, 1100, 1173, 1248, 1325, 1404, 1485, 1568, 1653, 1740, 1829, 1920, 2013, 2108, 2205, 2304, 2405, 2508, 2613, 2720, 2829, 2940, 3053, 3168, 3285, 3404, 3525

Offset: 0

Omar E. Pol, Aug 28 2007

G. C. Greubel, Table of n, a(n) for n = 0..5000
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
Cf. A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761.
Cf. A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769.

#(#+28)&/@Range[0,50] (* or *) LinearRecurrence[{3,-3,1},{0,29,60},50] (* Harvey P. Dale, Apr 30 2018 *)

a(n)=n*(n+28) \\ Charles R Greathouse IV, Jun 17 2017

[n*(n+28) for n in (0..50)] # G. C. Greubel, Mar 13 2022

a(n) = 2*n + a(n-1) + 27, with a(0)=0. - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(28)/28 = A001008(28)/A102928(28) = 315404588903/2248776129600, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 7751493599/321253732800. (End)
G.f.: x*(29 - 27*x)/(1-x)^3. - Harvey P. Dale, Aug 03 2021
E.g.f.: x*(29 + x)*exp(x). - G. C. Greubel, Mar 13 2022

A132771 a(n) = n*(n + 29).

Original entry on oeis.org

0, 30, 62, 96, 132, 170, 210, 252, 296, 342, 390, 440, 492, 546, 602, 660, 720, 782, 846, 912, 980, 1050, 1122, 1196, 1272, 1350, 1430, 1512, 1596, 1682, 1770, 1860, 1952, 2046, 2142, 2240, 2340, 2442, 2546, 2652, 2760, 2870, 2982, 3096, 3212, 3330, 3450, 3572

Offset: 0

Omar E. Pol, Aug 28 2007

G. C. Greubel, Table of n, a(n) for n = 0..5000
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
Cf. A098849, A098850, A098603, A098847, A098848, A102928, A120071, A132759, A132760, A132761.
Cf. A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769, A132770.

Table[n(n+29), {n,0,50}] (* Bruno Berselli, Apr 03 2015 *)
LinearRecurrence[{3,-3,1},{0,30,62},50] (* Harvey P. Dale, Oct 18 2024 *)

a(n)=n*(n+29) \\ Charles R Greathouse IV, Jun 17 2017

[n*(n+29) for n in (0..50)] # G. C. Greubel, Mar 13 2022

a(n) = 2*n + a(n-1) + 28 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(29)/29 = A001008(29)/A102928(29) = 9227046511387/67543597321200, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/29 - 236266661971/9649085331600. (End)
From G. C. Greubel, Mar 13 2022: (Start)
G.f.: 2*(15*x - 14*x^2)/(1-x)^3.
E.g.f.: x*(30 + x)*exp(x). (End)

A164009 Zero together with row 9 of the array in A163280.

Original entry on oeis.org

0, 19, 38, 51, 76, 75, 114, 105, 136, 162, 190, 209, 264, 273, 308, 345, 384, 425, 468, 513, 560, 609, 660, 713, 768, 825, 884, 945, 1008, 1073, 1140, 1209, 1280, 1353, 1428, 1505, 1584, 1665, 1748, 1833, 1920, 2009, 2100, 2193, 2288, 2385, 2484, 2585, 2688

Offset: 0

Omar E. Pol, Aug 08 2009

nonn

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

Cf. A008578, A161344, A161345, A163280, A164000, A164008, A164010.

A033676 := proc(n) local dvs; dvs := sort(convert(numtheory[divisors](n), list)) ; op(floor((nops(dvs)+1)/2) , dvs) ; end proc:
A163280 := proc(n, k) local r, T ; r := 0 ; for T from k^2 by k do if A033676(T) = k then r := r+1 ; if r = n then return T ; end if; end if; end do: end proc:
printf("0, ") ; for n from 1 to 90 do printf("%d, ", A163280(9, n)) ; end do ; # R. J. Mathar, Jul 31 2010

Conjecture: a(n) = A028566(n), n > 12. [R. J. Mathar, Jul 31 2010]

Terms beyond a(12) from R. J. Mathar, Jul 31 2010

A132772 a(n) = n*(n + 30).

Original entry on oeis.org

0, 31, 64, 99, 136, 175, 216, 259, 304, 351, 400, 451, 504, 559, 616, 675, 736, 799, 864, 931, 1000, 1071, 1144, 1219, 1296, 1375, 1456, 1539, 1624, 1711, 1800, 1891, 1984, 2079, 2176, 2275, 2376, 2479, 2584, 2691, 2800, 2911, 3024, 3139, 3256, 3375, 3496, 3619

Offset: 0

Omar E. Pol, Aug 28 2007

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566.
Cf. A028569, A067079, A098849, A098850, A098603, A098847, A098848, A102928, A120071.
Cf. A132759, A132760, A132761, A132762, A132763, A132764, A132765, A132766, A132767.
Cf. A132768, A132769, A132770, A132771.

Table[n(n+30),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,31,64},50] (* Harvey P. Dale, Mar 06 2015 *)

a(n)=n*(n+30) \\ Charles R Greathouse IV, Jun 17 2017

[n*(n+30) for n in (0..50)] # G. C. Greubel, Mar 13 2022

G.f.: x*(31-29*x)/(1-x)^3. - R. J. Mathar, Nov 14 2007
a(n) = 2*n + a(n-1) + 29 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(0)=0, a(1)=31, a(2)=64, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Mar 06 2015
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(30)/30 = A001008(30)/A102928(30) = 9304682830147/69872686884000, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 225175759291/9981812412000. (End)
E.g.f.: x*(31 + x)*exp(x). - G. C. Greubel, Mar 13 2022

A028568 Palindromes of the form k*(k+8).

Original entry on oeis.org

0, 9, 33, 4884, 8448, 9009, 31313, 48384, 52425, 82928, 88788, 489984, 505505, 861168, 5013105, 8020208, 48999984, 88322388, 801909108, 902101209, 3305445033, 4899999984, 8807447088, 35565056553, 52065656025, 58129692185, 80532223508, 88892229888, 357468864753

Offset: 1

Patrick De Geest

For i >= 0, 48(99)^{2*i}84 is a term arising from k = 69^i6, where ^ is repeated concatenation. - Michael S. Branicky, Jan 30 2022

Michael S. Branicky, Table of n, a(n) for n = 1..58
Patrick De Geest, Palindromic Quasipronics of the form n(n+x)

Intersection of A002113 and A028566.

Cf. A028567.

Select[Table[k(k+8),{k,0,600000}],PalindromeQ] (* Harvey P. Dale, Jun 24 2023 *)

a(n) = A028567(n) * (A028567(n) + 8). - Michael S. Branicky, Jan 30 2022

a(26) and beyond from Michael S. Branicky, Jan 30 2022

cp's OEIS Frontend

A098832 Square array read by antidiagonals: even-numbered rows of the table are of the form n*(n+m) and odd-numbered rows are of the form n*(n+m)/2.

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A132768 a(n) = n*(n + 26).

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A225948 a(0) = -1; for n>0, a(n) = numerator(1/4 - 4/n^2).

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A132769 a(n) = n*(n + 27).

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A105020 Array read by antidiagonals: row n (n >= 0) contains the numbers m^2 - n^2, m >= n+1.

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A132770 a(n) = n*(n + 28).

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A132771 a(n) = n*(n + 29).

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A098832 Square array read by antidiagonals: even-numbered rows of the table are of the form n(n+m) and odd-numbered rows are of the form n(n+m)/2.