A000466 -id:A000466 - cp's OEIS frontend

A070262 5th diagonal of triangle defined in A051537.

5, 3, 21, 2, 45, 15, 77, 6, 117, 35, 165, 12, 221, 63, 285, 20, 357, 99, 437, 30, 525, 143, 621, 42, 725, 195, 837, 56, 957, 255, 1085, 72, 1221, 323, 1365, 90, 1517, 399, 1677, 110, 1845, 483, 2021, 132, 2205, 575, 2397, 156, 2597, 675, 2805, 182, 3021, 783

Offset: 1

Amarnath Murthy, May 09 2002

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

Cf. A061037. [From R. J. Mathar, Sep 29 2008]
Cf. A010873, A051537.
Cf. A000466, A002378, A003185, A085027.

[LCM(n + 4, n)/GCD(n + 4, n): n in [1..50]]; // G. C. Greubel, Sep 20 2018

Table[ LCM[i + 4, i] / GCD[i + 4, i], {i, 1, 60}]
LinearRecurrence[{0,0,0,3,0,0,0,-3,0,0,0,1},{5,3,21,2,45,15,77,6,117,35,165,12},90] (* Harvey P. Dale, Jul 13 2019 *)

Vec(x*(5 + 3*x + 21*x^2 + 2*x^3 + 30*x^4 + 6*x^5 + 14*x^6 - 3*x^8 - x^9 - 3*x^10) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3) + O(x^60)) \\ Colin Barker, Mar 27 2017

a(n) = lcm(n+4,n)/gcd(n+4,n); \\ Altug Alkan, Sep 20 2018

a(n) = lcm(n + 4, n) / gcd(n + 4, n).
From Colin Barker, Mar 27 2017: (Start)
G.f.: x*(5 + 3*x + 21*x^2 + 2*x^3 + 30*x^4 + 6*x^5 + 14*x^6 - 3*x^8 - x^9 - 3*x^10) / ((1 - x)^3*(1 + x)^3*(1 + x^2)^3).
a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12) for n>12. (End)
From Luce ETIENNE, May 10 2018: (Start)
a(n) = n*(n+4)*4^((5*(n mod 4)^3 - 24*(n mod 4)^2 + 31*(n mod 4)-12)/6).
a(n) = n*(n+4)*(37-27*cos(n*Pi)-6*cos(n*Pi/2))/64. (End)
From Amiram Eldar, Oct 08 2023: (Start)
Sum_{n>=1} 1/a(n) = 11/6.
Sum_{n>=1} (-1)^n/a(n) = 7/6.
Sum_{k=1..n} a(k) ~ (37/192) * n^3. (End)

Edited by Robert G. Wilson v, May 10 2002

A142717 First (leftmost) odd term in the n-th row of triangle A120070.

Original entry on oeis.org

3, 5, 15, 21, 35, 45, 63, 77, 99, 117, 143, 165, 195, 221, 255, 285, 323, 357, 399, 437, 483, 525, 575, 621, 675, 725, 783, 837, 899, 957, 1023, 1085, 1155, 1221, 1295, 1365, 1443, 1517, 1599, 1677, 1763, 1845, 1935, 2021, 2115, 2205, 2303, 2397, 2499, 2597

Offset: 1

Paul Curtz, Sep 26 2008

nonn

Also: Records sequence of A100181.

The last (rightmost) term in the n-th row of triangle A120070 is A005408(n).

			The odd terms of A120070 build the irregular triangle
  3;
  5;
  15,7;
  21,9;
  35,27,11;
  45,33,13;
  63,55,39,15;
The leftmost column defines this sequence.

Paolo Xausa, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Cf. A000466, A078371, A100181.

A142717[n_]:=(n+1)^2-If[OddQ[n],1,4];Array[A142717,100] (* or *)
LinearRecurrence[{2,0,-2,1},{3,5,15,21},100] (* Paolo Xausa, Dec 05 2023 *)

First differences: a(n+1)-a(n) = A142954(n).
From R. J. Mathar, Oct 24 2008: (Start)
a(n) = (n+1)^2-1 = A000466((n+1)/2) if n odd.
a(n) = (n+1)^2-4 = A078371(n/2-1) if n even.
a(n) = 2*a(n-1) -2*a(n-3) +a(n-4).
G.f.: x(3-x+5x^2-3x^3)/((1+x)(1-x)^3). (End)

Edited and extended by R. J. Mathar, Oct 24 2008

A302488 Total domination number of the n X n grid graph.

Original entry on oeis.org

0, 1, 2, 3, 6, 9, 12, 15, 20, 25, 30, 35, 42, 49, 56, 63, 72, 81, 90, 99, 110, 121, 132, 143, 156, 169, 182, 195, 210, 225, 240, 255, 272, 289, 306, 323, 342, 361, 380, 399, 420, 441, 462, 483, 506, 529, 552, 575, 600, 625, 650, 675, 702, 729, 756, 783, 812, 841, 870, 899, 930

Offset: 0

Eric W. Weisstein, Apr 08 2018

Extended to a(0) and a(1) using the formula/recurrence. The total domination number of the 1 X 1 grid graph is undefined.

Andrew Howroyd, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Grid Graph.
Eric Weisstein's World of Mathematics, Total Domination Number.
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Main diagonal of A300358.
The four quadrasections are A002943, A016754, A002939(n+1), A000466(n+1).
Bisections are A002378 and A085046.
Cf. A303142.

R:=RealField(); [Round(((-1)^n + 2*n*(n + 2) + 4*Sin(n*Pi(R)/2) - 1)/8): n in [0..30]]; // G. C. Greubel, Apr 09 2018

Table[(-1 + (-1)^n + 2 n (2 + n) + 4 Sin[n Pi/2])/8, {n, 0, 20}]
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {0, 1, 2, 3, 6, 9}, 20]
CoefficientList[Series[x (-1 - 2 x^3 + x^4)/((-1 + x)^3 (1 + x + x^2 + x^3)), {x, 0, 20}], x]

for(n=0,30, print1(round(((-1)^n + 2*n*(n + 2) + 4*sin(n*Pi/2) - 1)/8), ", ")) \\ G. C. Greubel, Apr 09 2018

a(n)=my(m=n\4); (2*m+1)*(2*m + n%4) \\ Andrew Howroyd, Aug 17 2025

a(n) = ((-1)^n + 2*n*(n + 2) + 4*sin(n*Pi/2) - 1)/8.
a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6).
G.f.: x*(1 + 2*x^3 - x^4)/((1 - x)^3*(1 + x + x^2 + x^3)).
a(4*m + r) = (2*m + 1)*(2*m + r) for 0 <= r < 4. - Charles Kusniec, Aug 16 2025
From Amiram Eldar, Aug 26 2025: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/8 + 3/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/8 - 1/2. (End)

a(0)=0 prepended and offset corrected by Andrew Howroyd, Aug 17 2025

A069075 a(n) = (4*n^2 - 1)^2.

Original entry on oeis.org

1, 9, 225, 1225, 3969, 9801, 20449, 38025, 65025, 104329, 159201, 233289, 330625, 455625, 613089, 808201, 1046529, 1334025, 1677025, 2082249, 2556801, 3108169, 3744225, 4473225, 5303809, 6245001, 7306209, 8497225, 9828225, 11309769

Offset: 0

Benoit Cloitre, Apr 05 2002

Products of squares of 2 successive odd numbers. - Peter Munn, Nov 17 2019

L. B. W. Jolley, Summation of Series, Dover, 1961.
Konrad Knopp, Theory and application of infinite series, Dover, 1990, p. 269.

Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A000466, A123092, A166329.

(4*Range[0,30]^2-1)^2 (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,9,225,1225,3969},30] (* Harvey P. Dale, Feb 23 2018 *)

Sum_{n>=1} 1/a(n) = (Pi^2 - 8)/16 = 0.1168502750680... (A123092) [Jolley eq. 247]
G.f.: (-1 - 4*x - 190*x^2 - 180*x^3 - 9*x^4) / (x-1)^5. - R. J. Mathar, Oct 03 2011
a(n) = A000466(n)^2. - Peter Munn, Nov 17 2019
E.g.f.: exp(x)*(1 + 8*x + 104*x^2 + 96*x^3 + 16*x^4). - Stefano Spezia, Nov 17 2019
Sum_{n>=0} (-1)^n/a(n) = Pi/8 + 1/2. - Amiram Eldar, Feb 08 2022

A085027 a(n) = (4n+3)(4*n+7).

Original entry on oeis.org

21, 77, 165, 285, 437, 621, 837, 1085, 1365, 1677, 2021, 2397, 2805, 3245, 3717, 4221, 4757, 5325, 5925, 6557, 7221, 7917, 8645, 9405, 10197, 11021, 11877, 12765, 13685, 14637, 15621, 16637, 17685, 18765, 19877, 21021, 22197, 23405, 24645, 25917, 27221, 28557, 29925, 31325, 32757, 34221

Offset: 0

Gary W. Adamson, Jun 19 2003

1 = 3/7 + Sum_{n>=1} 16/a(n) = 3/7 + 16/77 + 16/165 + 16/285...+...; with partial sums: 3/7, 7/11, 11/15, 15/19, 19/23, ...(4n+3)/(4n+7), ... ==> 1.
With A003185(n) = (4*n+1)*(4*n+5), a bisection of A078371(n) which is a bisection of A061037(n+2).
A quadrisection of A061037(n+2). After A002378(n), A003185(n) and A000466(n+1). - Paul Curtz, Mar 30 2011

			21 = (3)(7), 77 = (7)(11), 165 = (11)(15), 285 = (15)(19), 437 = (19)(23)...

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

Cf. A000466, A002378, A003185, A061037, A078371.

[16*n^2+40*n+21: n in [0..35]]; // Vincenzo Librandi, Aug 13 2011

Mathematica
```
Table[(4*n + 3) (4*n + 7), {n, 0, 45}]
```

a(n)=(4*n+3)*(4*n+7) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 16*n^2+40*n+21. - Vincenzo Librandi, Aug 13 2011
From Colin Barker, Jul 11 2012: (Start)
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: (21+14*x-3*x^2)/(1-x)^3. (End)
E.g.f.: (21 +56*x +16*x^2)*exp(x). - G. C. Greubel, Sep 20 2018
From Amiram Eldar, Oct 08 2023: (Start)
Sum_{n>=0} 1/a(n) = 1/12.
Sum_{n>=0} (-1)^n/a(n) = Pi/(8*sqrt(2)) + log(sqrt(2)-1)/(4*sqrt(2)) - 1/12. (End)

A198148 a(n) = n(n+2)(9 - 7*(-1)^n)/16.

Original entry on oeis.org

0, 3, 1, 15, 3, 35, 6, 63, 10, 99, 15, 143, 21, 195, 28, 255, 36, 323, 45, 399, 55, 483, 66, 575, 78, 675, 91, 783, 105, 899, 120, 1023, 136, 1155, 153, 1295, 171, 1443, 190, 1599, 210, 1763, 231, 1935, 253, 2115, 276, 2303, 300, 2499, 325

Offset: 0

Paul Curtz, Oct 21 2011

See, in A181318(n), A060819(n)*A060819(n+p): A060819(n)^2, A064038(n), a(n), A160050(n), A061037(n), A178242(n). The second differences a(n+2)-2*a(n+1)+a(n) = -5, 16, -26, 44, -61, 86, -110, 142, -173, 212, -250, 296, -341, 394, -446, 506, taken modulo 9 are periodic with the palindromic period 4, 7, 1, 8, 2, 5, 7, 7, 7, 5, 2, 8, 1, 7, 4.

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

Cf. quadrisections A014105, A001539, A000384, A141759.

Cf. A060819, A000217, A000466, A142705, A000034, A005563, A010689, A028552, A050534.

List([0..60], n -> n*(n+2)*(9-7*(-1)^n)/16); # G. C. Greubel, Feb 21 2019

[n*(n+2)*(9-7*(-1)^n)/16: n in [0..60]]; // Vincenzo Librandi, Nov 25 2011

A198148:=n->n*(n+2)*(9-7*(-1)^n)/16; seq(A198148(k), k=0..100); # Wesley Ivan Hurt, Oct 16 2013

LinearRecurrence[{0,3,0,-3,0,1},{0,3,1,15,3,35},60] (* Vincenzo Librandi, Nov 25 2011 *)

a(n)=n*(n+2)*(9-7*(-1)^n)/16 \\ Charles R Greathouse IV, Oct 16 2015

[n*(n+2)*(9-7*(-1)^n)/16 for n in (0..60)] # G. C. Greubel, Feb 21 2019

a(n) = A060819(n)*A060819(n+2).
a(2n) = n*(n+1)/2 = A000217(n).
a(2n+1) = (2*n+1)*(2*n+3) = A000466(n+1).
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6), n>5.
a(n+1) - a(n) = (7*(-1)^n *(2*n^2+6*n+3) +18*n +27)/16.
a(n) = A142705(n) / A000034(n+1).
a(n) = A005563(n) / A010689(n+1). - Franklin T. Adams-Watters, Oct 21 2011
G.f. x*(3 +x +6*x^2 -x^4)/(1-x^2)^3. - R. J. Mathar, Oct 25 2011
a(n)*a(n+1) = a(A028552(n)) = A050534(n+2). - Bruno Berselli, Oct 26 2011
a(n) = numerator( binomial((n+2)/2,2) ). - Wesley Ivan Hurt, Oct 16 2013
E.g.f.: x*((24+x)*cosh(x) + (3+8*x)*sinh(x))/8. - G. C. Greubel, Sep 20 2018
Sum_{n>=1} 1/a(n) = 5/2. - Amiram Eldar, Aug 12 2022

A226023 A142705 (numerators of 1/4-1/(4n^2)) sorted to natural order.

Original entry on oeis.org

0, 2, 3, 6, 12, 15, 20, 30, 35, 42, 56, 63, 72, 90, 99, 110, 132, 143, 156, 182, 195, 210, 240, 255, 272, 306, 323, 342, 380, 399, 420, 462, 483, 506, 552, 575, 600, 650, 675, 702, 756, 783, 812, 870, 899

Offset: 0

Paul Curtz, May 23 2013

A198442(n) without indices 4*n+2.
a(n)/A130823(n+1) = 0, 2,3,2, 4,5,4, 6,7,6, 8,9,8, ... (equal to A133310+1, after 0; see also A008611).
-1,   0,   2,   3, is divisible by  1 (for a(-1)=-1),
3,    6,  12,  15,                  3,
15,  20,  30,  35                   5,
35,  42,  56,  63                   7,
63,  72,  90,  99                   9,
99, 110, 132, 143,                 11, etc.
First column:  A000466(n),
second column: A002943(n),
third column:  A002939(n+1),
fourth column: A000466(n+1).
a(n) is also the numerator of 1/4-1/(4*n+2)^2: 0/1, 2/9, 3/16, 6/25, 12/49, 15/64, 20/81, 30/121, 35/144, 42/169, 56/225,...
The n-th denominator is equal to 4*a(n) + A146325(n+2).
Note that the differences of a(n-1): 1, 2, 1, 3, 6, 3, 5, 10, 5, 7, 14, 7, 9, 18, 9, 11, 22,... (from A043547 by pairs and 2*n+1) has the same recurrence.
(Of course every sequence which obeys a linear recurrence with constant coefficients has first differences that obey the same linear recurrence. - R. J. Mathar, Jun 14 2013)

Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Trisections: A002939, A000466, A002943.

A226023 := proc(n)
    option remember;
    if n <=6 then
        op(n+1,[0,2,3,6,12,15,20]) ;
    else
        procname(n-1)+2*procname(n-3)-2*procname(n-4)-procname(n-6)+procname(n-7) ;
    end if;
end proc: # R. J. Mathar, Jun 28 2013

A226023[n_]:=Floor[(2n+1)/3]Floor[(2n+5)/3];
Array[A226023,100,0] (* Paolo Xausa, Dec 05 2023 *)

a(n) = floor( (2*n + 1)/3 ) * floor( (2*n + 5)/3 ) = A004396(n) * A004396(n+2).
Recurrences: a(n) = 3*a(n-3) -3*a(n-6) +a(n-9) = a(n-1) +2*a(n-3) -2*a(n-4) -a(n-6) +a(n-7).
a(n+15)  - a(n) = 10*A042968(n+8).
a(n+1) - a(n-2) = 2*A042968(n) with a(-2)=0, a(-1)=-1.
G.f.: x*(2+x+3*x^2+2*x^3+x^4-x^5)/((1-x)^3 * (1+x+x^2)^2). [Ralf Stephan, May 24 2013]

A070260 Third diagonal of triangle defined in A051537.

Original entry on oeis.org

3, 2, 15, 6, 35, 12, 63, 20, 99, 30, 143, 42, 195, 56, 255, 72, 323, 90, 399, 110, 483, 132, 575, 156, 675, 182, 783, 210, 899, 240, 1023, 272, 1155, 306, 1295, 342, 1443, 380, 1599, 420, 1763, 462, 1935, 506, 2115, 552, 2303, 600, 2499, 650, 2703, 702

Offset: 1

Amarnath Murthy, May 09 2002

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

Bisections: A002378, A000466.

Cf. A051537.

Table[ LCM[i + 2, i] / GCD[i + 2, i], {i, 1, 60}]
LinearRecurrence[{0,3,0,-3,0,1},{3,2,15,6,35,12},60] (* Harvey P. Dale, Sep 14 2019 *)

Vec(x*(3+2*x+6*x^2-x^4) / (1-x^2)^3 + O(x^60)) \\ Colin Barker, Mar 27 2017

From Vladeta Jovovic, May 09 2002: (Start)
a(n) = n*(n+2)/4 if n is even else n*(n+2).
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
G.f.: x*(3 + 2*x + 6*x^2 - x^4)/(1 - x^2)^3. (End)
E.g.f.: (x/4)*((12 + x)*cosh(x) + (3 + 4*x)*sinh(x)). - G. C. Greubel, Jul 20 2017
From Amiram Eldar, Oct 08 2023: (Start)
Sum_{n>=1} 1/a(n) = 3/2.
Sum_{n>=1} (-1)^n/a(n) = 1/2.
Sum_{k=1..n} a(k) ~ (5/24) * n^3. (End)

More terms from Vladeta Jovovic, May 09 2002

A108100 a(n) = (2n-1)^2 + (2n+1)^2.

Original entry on oeis.org

2, 10, 34, 74, 130, 202, 290, 394, 514, 650, 802, 970, 1154, 1354, 1570, 1802, 2050, 2314, 2594, 2890, 3202, 3530, 3874, 4234, 4610, 5002, 5410, 5834, 6274, 6730, 7202, 7690, 8194, 8714, 9250, 9802, 10370, 10954, 11554, 12170, 12802, 13450, 14114, 14794, 15490

Offset: 0

Dorthe Roel (dorthe_roel(AT)hotmail.com or dorthe.roel1(AT)skolekom.dk), Jun 07 2005

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

Apart from leading term, same as A008527.

Cf. A000466, A016754, A053755, A158444.

[8*n^2+2: n in [0..50]]; // Vincenzo Librandi, Sep 06 2011

Table[8n^2+2,{n,0,50}]  (* Harvey P. Dale, Feb 20 2011 *)

makelist(8*n^2+2,n,0,30); /* Martin Ettl, Nov 12 2012 */

a(n)=(2*n-1)^2+(2*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

From R. J. Mathar, Aug 24 2008: (Start)
O.g.f.: 2*(1 + 2*x + 5*x^2)/(1-x)^3.
a(n) = 2*A053755(n). (End)
a(n) = a(-n); a(n) + a(-n) = A158444(n). - Bruno Berselli, Sep 06 2011
a(n) = 2*(A000466(n) + 2). - Martin Ettl, Nov 12 2012
From Elmo R. Oliveira, Nov 16 2024: (Start)
E.g.f.: 2*exp(x)*(1 + 4*x + 4*x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A158443 a(n) = 16*n^2 - 4.

Original entry on oeis.org

12, 60, 140, 252, 396, 572, 780, 1020, 1292, 1596, 1932, 2300, 2700, 3132, 3596, 4092, 4620, 5180, 5772, 6396, 7052, 7740, 8460, 9212, 9996, 10812, 11660, 12540, 13452, 14396, 15372, 16380, 17420, 18492, 19596, 20732, 21900, 23100, 24332, 25596, 26892, 28220, 29580

Offset: 1

Vincenzo Librandi, Mar 19 2009

The identity (8*n^2 - 1)^2 - (16*n^2 - 4) *(2*n)^2 = 1 can be written as A157914(n)^2 - a(n)*A005843(n)^2 = 1.

Sequence found by reading the line from 12, in the direction 12, 60, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000466, A005843, A074377, A157914.

I:=[12, 60, 140]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]];

16Range[60]^2-4  (* Harvey P. Dale, Mar 18 2011 *)

PARI
```
a(n) = 16*n^2 - 4.
```

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f: 4*x*(3+6*x-x^2)/(1-x)^3.
From Amiram Eldar, Mar 05 2023: (Start)
Sum_{n>=1} 1/a(n) = 1/8.
Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi-2)/16. (End)
From Elmo R. Oliveira, Jan 16 2025: (Start)
E.g.f.: 4*(exp(x)*(4*x^2 + 4*x - 1) + 1).
a(n) = 4*A000466(n). (End)

cp's OEIS Frontend

A070262 5th diagonal of triangle defined in A051537.

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A142717 First (leftmost) odd term in the n-th row of triangle A120070.

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A302488 Total domination number of the n X n grid graph.

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A069075 a(n) = (4*n^2 - 1)^2.

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A085027 a(n) = (4*n+3)*(4*n+7).

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A198148 a(n) = n*(n+2)*(9 - 7*(-1)^n)/16.

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Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A226023 A142705 (numerators of 1/4-1/(4n^2)) sorted to natural order.

A085027 a(n) = (4n+3)(4*n+7).

A198148 a(n) = n(n+2)(9 - 7*(-1)^n)/16.

A108100 a(n) = (2n-1)^2 + (2n+1)^2.