A118120 -id:A118120 - cp's OEIS frontend

A118673 Positive solutions x to the equation x^2 + (x+71)^2 = y^2.

0, 13, 160, 213, 280, 1113, 1420, 1809, 6660, 8449, 10716, 38989, 49416, 62629, 227416, 288189, 365200, 1325649, 1679860, 2128713, 7726620, 9791113, 12407220, 45034213, 57066960, 72314749, 262478800, 332610789, 421481416, 1529838729, 1938597916, 2456573889

Offset: 0

Mohamed Bouhamida, May 19 2006

Consider all Pythagorean triples (x,x+71,y) ordered by increasing y; sequence gives x values.
For the generic case x^2+(x+p)^2=y^2 with p=2*m^2-1 a prime number in A066436, m>=2 the associated value in A066049, the x values are given by the sequence defined by: a(n) = 6*a(n-3) -a(n-6) + 2*p with a(0)=0, a(1)=2m+1, a(2)=6m^2-10m+4, a(3)=3p, a(4)=6m^2+10m+4, a(5)=40m^2-58m+21.
For the generic case x^2+(x+p)^2=y^2 with p=2*m^2-1 a prime number in A066436, m>=2, Y values are given by the sequence defined by: b(n)=6*b(n-3)-b(n-6) with b(0)=p, b(1)=2m^2+2m+1, b(2)=10m^2-14m+5, b(3)=5p, b(4)=10m^2+14m+5, b(5)=58m^2-82m+29. - Mohamed Bouhamida, Sep 09 2009

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,6,-6,0,-1,1).

Cf. A076296 (p=7), A118120 (p=17), A118674 (p=31), A129836 (p=97), A129992 (p=127), A129993 (p=199), A129991 (p=241), A129999 (p=337), A130004 (p=449), A130005 (p=577), A130013 (p=647), A130014 (p=881), A130017 (p=967).

m:=25; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(13+147*x+53*x^2-11*x^3-49*x^4-11*x^5)/((1-x)*(1 - 6*x^3 +x^6)))); // G. C. Greubel, May 07 2018

Select[Range[0,100000],IntegerQ[Sqrt[#^2+(#+71)^2]]&] (* or *) LinearRecurrence[{1,0,6,-6,0,-1,1},{0,13,160,213,280,1113,1420},100] (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)

a(n)=([0,1,0,0,0,0,0; 0,0,1,0,0,0,0; 0,0,0,1,0,0,0; 0,0,0,0,1,0,0; 0,0,0,0,0,1,0; 0,0,0,0,0,0,1; 1,-1,0,-6,6,0,1]^n*[0;13;160;213;280;1113;1420])[1,1] \\ Charles R Greathouse IV, Apr 22 2016

x='x+O('x^30); concat([0], Vec(x*(13+147*x+53*x^2-11*x^3 -49*x^4 -11*x^5)/((1-x)*(1-6*x^3+x^6)))) \\ G. C. Greubel, May 07 2018

a(n) = 6*a(n-3) -a(n-6) +142 with a(0)=0, a(1)=13, a(2)=160, a(3)=213, a(4)=280, a(5)=1113.

O.g.f.: x*(13+147*x+53*x^2-11*x^3-49*x^4-11*x^5)/((1-x)*(1-6*x^3+x^6)). - R. J. Mathar, Jun 10 2008

Edited by R. J. Mathar, Jun 10 2008

A155923 Positive numbers y such that y^2 is of the form x^2+(x+17)^2 with integer x.

Original entry on oeis.org

13, 17, 25, 53, 85, 137, 305, 493, 797, 1777, 2873, 4645, 10357, 16745, 27073, 60365, 97597, 157793, 351833, 568837, 919685, 2050633, 3315425, 5360317, 11951965, 19323713, 31242217, 69661157, 112626853, 182092985, 406014977, 656437405

Offset: 1

Klaus Brockhaus, Feb 09 2009

(-5,a(1)) and (A118120(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+17)^2 = y^2. (Offset 1 is assumed for A118120.)
lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = (19+6*sqrt(2))/17 for n mod 3 = {0, 2}.
lim_{n -> infinity} a(n)/a(n-1) = (387+182*sqrt(2))/17^2 for n mod 3 = 1.
For the generic case x^2+(x+p)^2=y^2 with p=2*m^2-1 a prime number in A066436, m>=2, the x values are given by the sequence defined by: a(n)=6*a(n-3)-a(n-6)+2p with a(1)=0, a(2)=2m+1, a(3)=6m^2-10m+4, a(4)=3p, a(5)=6m^2+10m+4, a(6)=40m^2-58m+21.Y values are given by the sequence defined by: b(n)=6*b(n-3)-b(n-6) with b(1)=p, b(2)=2*m^2+2m+1, b(3)=10m^2-14m+5, b(4)=5p, b(5)=10m^2+14m+5, b(6)=58m^2-82m+29. [From Mohamed Bouhamida, Sep 09 2009]

			(-5,a(1)) = (-5,13) is a solution: (-5)^2+(-5+17)^2 = 25+144 = 169 = 13^2;
(A118120(1), a(2)) = (0, 17) is a solution: 0^2+(0+17)^2 = 289 = 17^2;
(A118120(2), a(3)) = (7, 25) is a solution: 7^2+(7+17)^2 = 49+576 = 625 = 25^2.

Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-1).

Cf. A118120, A156035 (decimal expansion of 3+2*sqrt(2)), A156163 (decimal expansion of (19+6*sqrt(2))/17), A157649 (decimal expansion of (387+182*sqrt(2))/17^2).

Cf. A156156 (first trisection), A156157 (second trisection), A156158 (third trisection).

LinearRecurrence[{0,0,6,0,0,-1},{13,17,25,53,85,137},50] (* Harvey P. Dale, Feb 11 2015 *)

{forstep(n=-5, 660000000, [1,3], if(issquare(2*n*(n+17)+289, &k), print1(k, ",")))}

a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1) = 13, a(2) = 17, a(3) = 25, a(4) = 53, a(5) = 85, a(6) = 137.

G.f.: x*(1-x)*(13+30*x+55*x^2+30*x^3+13*x^4)/(1-6*x^3+x^6).

G.f. corrected, first and fourth comment and examples edited, cross-reference added by Klaus Brockhaus, Sep 22 2009

A155464 a(n) = 7a(n-1) - 7a(n-2) + a(n-3) for n > 2; a(0) = 0, a(1) = 51, a(2) = 340.

Original entry on oeis.org

0, 51, 340, 2023, 11832, 69003, 402220, 2344351, 13663920, 79639203, 464171332, 2705388823, 15768161640, 91903581051, 535653324700, 3122016367183, 18196444878432, 106056652903443, 618143472542260, 3602804182350151

Offset: 0

Klaus Brockhaus, Jan 30 2009

lim_{n -> infinity} a(n+1)/a(n) = 3+2*sqrt(2).

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

First trisection of A118120. Equals 17*A001652.

Cf. A155465, A155466, A156035 (decimal expansion of 3+2*sqrt(2)).

I:=[0,51,340]; [n le 3 select I[n] else 7*Self(n-1) - 7*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Aug 21 2018

LinearRecurrence[{7,-7,1},{0,51,340},30] (* Harvey P. Dale, Jun 10 2013 *)
Table[17*(LucasL[2*n+1,2] - 2)/4, {n, 0, 50}] (* G. C. Greubel, Aug 21 2018 *)

{m=20; v=concat([0, 51, 340], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}

a(n) = 6*a(n-1) - a(n-2) + 34 for n > 1; a(0) = 0, a(1) = 51.
a(n) = ((1+sqrt(2))*(3+2*sqrt(2))^n + (1-sqrt(2))*(3-2*sqrt(2))^n -2)*(17/4).
G.f.: 17*x*(3-x)/((1-x)*(1-6*x+x^2)).
a(n) = 17*(A002203(2*n+1) - 2)/4. - G. C. Greubel, Aug 21 2018

Comment and recursion formula added, cross-references edited by Klaus Brockhaus, Sep 23 2009

A155465 a(n) = 7a(n-1) - 7a(n-2) + a(n-3) for n > 2; a(0) = 7, a(1) = 88, a(2) = 555.

Original entry on oeis.org

7, 88, 555, 3276, 19135, 111568, 650307, 3790308, 22091575, 128759176, 750463515, 4374021948, 25493668207, 148587987328, 866034255795, 5047617547476, 29419671029095, 171470408627128, 999402780733707, 5824946275775148

Offset: 0

Klaus Brockhaus, Jan 30 2009

lim_{n -> infinity} a(n+1)/a(n) = 3+2*sqrt(2).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Second trisection of A118120. Cf. A001652.

Cf. A155464, A155466, A156035 (decimal expansion of 3+2*sqrt(2)).

I:=[7,88,555]; [n le 3 select I[n] else 7*Self(n-1) - 7*Self(n-2) + Self(n-3): n in [1..50]]; // G. C. Greubel, Aug 21 2018

LinearRecurrence[{7,-7,1},{7,88,555},30] (* Harvey P. Dale, Apr 29 2012 *)
Table[(3*LucasL[2*n+3,2] + 10*LucasL[2*n+1,2] - 34)/4, {n, 0, 50}] (* G. C. Greubel, Aug 21 2018 *)

{m=20; v=concat([7, 88, 555], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}

a(n) = 6*a(n-1) - a(n-2) + 34 for n > 1; a(0) = 7, a(1) = 88.
a(n) = ((31+25*sqrt(2))*(3+2*sqrt(2))^n + (31-25*sqrt(2))*(3-2*sqrt(2))^n - 34)/4.
G.f.: (7+39*x-12*x^2)/((1-x)*(1-6*x+x^2)).
a(n) = (3*A002203(2*n+3) + 10*A002203(2*n+1) - 34)/4. - G. C. Greubel, Aug 21 2018

Comment and recursion formula added, cross-references edited by Klaus Brockhaus, Sep 23 2009

A155466 a(n) = 7a(n-1) - 7a(n-2) + a(n-3) for n > 2; a(0) = 28, a(1) = 207, a(2) = 1248.

Original entry on oeis.org

28, 207, 1248, 7315, 42676, 248775, 1450008, 8451307, 49257868, 287095935, 1673317776, 9752810755, 56843546788, 331308470007, 1931007273288, 11254735169755, 65597403745276, 382329687301935, 2228380720066368

Offset: 0

Klaus Brockhaus, Jan 30 2009

lim_{n -> infinity} a(n+1)/a(n) = 3+2*sqrt(2).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Third trisection of A118120. Cf. A001652.

Cf. A155464, A155465, A156035 (decimal expansion of 3+2*sqrt(2)).

I:=[28, 207, 1248]; [n le 3 select I[n] else 7*Self(n-1) - 7*Self(n-2) + Self(n-3): n in [1..50]]; // G. C. Greubel, Aug 21 2018

Table[(10*LucasL[2*n+3,2] + 3*LucasL[2*n+1, 2] -34)/4, {n, 0, 50}] (* or *) LinearRecurrence[{7,-7,1}, {28, 207, 1248}, 50] (* G. C. Greubel, Aug 21 2018 *)

{m=19; v=concat([28, 207, 1248], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}

a(n) = 6*a(n-1) - a(n-2) + 34 for n > 1; a(0) = 28, a(1) = 207.
a(n) = ((73+53*sqrt(2))*(3+2*sqrt(2))^n + (73-53*sqrt(2))*(3-2*sqrt(2))^n - 34)/4.
G.f.: (28+11*x-5*x^2)/((1-x)*(1-6*x+x^2)).
a(n) = (10*A002203(2*n+3) + 3*A002203(2*n+1) - 34)/4. - G. C. Greubel, Aug 21 2018

Comment and recursion formula added, cross-references edited by Klaus Brockhaus, Sep 23 2009

A156159 Squares of the form k^2+(k+17)^2 with integer k.

Original entry on oeis.org

169, 289, 625, 2809, 7225, 18769, 93025, 243049, 635209, 3157729, 8254129, 21576025, 107267449, 280395025, 732947329, 3643933225, 9525174409, 24898630849, 123786459889, 323575532569, 845820499225, 4205095700689

Offset: 1

Klaus Brockhaus, Feb 09 2009

Square roots of k^2+(k+17)^2 are in A155923, values k (except for -5) are in A118120.

			625 = 25^2 is of the form k^2+(k+17)^2 with k = 7: 7^2+24^2 = 625. Hence 625 is in the sequence.

Index entries for linear recurrences with constant coefficients, signature (1,0,34,-34,0,-1,1).

Equals A155923^2. Cf. A156160 (first trisection), A156161 (second trisection), A156162 (third trisection).

Cf. A118120, A156035 (decimal expansion of 3+2*sqrt(2)), A156164 (decimal expansion of 17+12*sqrt(2)), A156163 (decimal expansion of (19+6*sqrt(2))/17), A157649 (decimal expansion of (387+182*sqrt(2))/17^2).

LinearRecurrence[{1,0,34,-34,0,-1,1},{169,289,625,2809,7225,18769,93025},30] (* Harvey P. Dale, Apr 22 2022 *)

{forstep(n=-5, 1600000, [1, 3], if(issquare(a=2*n*(n+17)+289), print1(a, ",")))}

a(n) = 34*a(n-3)-a(n-6)-2312 for n > 6; a(1)=169, a(2)=289, a(3)=625, a(4)=2809, a(5)=7225, a(6)=18769.
G.f.: x*(169+120*x+336*x^2-3562*x^3+336*x^4+120*x^5+169*x^6)/((1-x)*(1-34*x^3+x^6)).
Limit_{n -> oo} a(n)/a(n-3) = (17+12*sqrt(2)).
Limit_{n -> oo} a(n)/a(n-1) = ((19+6*sqrt(2))/17)^2 for n mod 3 = {0, 2}.
Limit_{n -> oo} a(n)/a(n-1) = ((387+182*sqrt(2))/17^2)^2 for n mod 3 = 1.

G.f. corrected, fourth comment and cross-references edited by Klaus Brockhaus, Sep 23 2009

A157649 Decimal expansion of (387 + 182*sqrt(2))/17^2.

Original entry on oeis.org

2, 2, 2, 9, 7, 1, 2, 3, 4, 7, 2, 3, 8, 4, 1, 9, 7, 1, 9, 3, 1, 4, 5, 5, 8, 2, 9, 6, 9, 0, 7, 1, 4, 5, 5, 0, 2, 7, 6, 7, 0, 5, 9, 7, 9, 6, 9, 5, 0, 1, 8, 8, 7, 5, 1, 9, 6, 5, 9, 3, 6, 7, 2, 0, 8, 1, 0, 7, 7, 2, 7, 0, 2, 6, 9, 9, 3, 2, 0, 0, 0, 3, 7, 0, 5, 0, 8, 8, 3, 4, 3, 4, 1, 7, 4, 0, 7, 4, 9, 5, 6, 3, 2, 4, 3

Offset: 1

Klaus Brockhaus, Mar 11 2009

Lim_{n -> infinity} b(n)/b(n-1) = (387 + 182*sqrt(2))/17^2 for n mod 3 = 1, b = A155923.

			(387 + 182*sqrt(2))/17^2 = 2.22971234723841971931...

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A118120, A155923, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A156163 (decimal expansion of (19+6*sqrt(2))/17).

SetDefaultRealField(RealField(100)); (387 + 182*Sqrt(2))/17^2; // G. C. Greubel, Aug 17 2018

RealDigits[(387 + 182*Sqrt[2])/17^2, 10, 100][[1]] (* G. C. Greubel, Aug 17 2018 *)

(387 + 182*sqrt(2))/17^2 \\ G. C. Greubel, Aug 17 2018

Equals (26 + 7*sqrt(2))/(26 - 7*sqrt(2)) = (3 + 2*sqrt(2))/((19 + 6*sqrt(2))/17)^2 = (3 + 2*sqrt(2))*(6 - sqrt(2))^2/(6 + sqrt(2))^2.

A129010 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+833)^2 = y^2.

Original entry on oeis.org

0, 124, 168, 187, 343, 399, 595, 624, 915, 952, 1260, 1372, 1768, 1827, 1975, 2499, 3135, 3367, 3468, 4312, 4620, 5712, 5875, 7524, 7735, 9499, 10143, 12427, 12768, 13624, 16660, 20352, 21700, 22287, 27195, 28987, 35343, 36292, 45895, 47124

Offset: 1

Mohamed Bouhamida, May 27 2007

nonn

Also values x of Pythagorean triples (x, x+833, y); 833=7^2*17.
Corresponding values y of solutions (x, y) are in A156835.
lim_{n -> infinity} a(n)/a(n-15) = 3+2*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = ((9+4*sqrt(2))/7)^2*((19+6*sqrt(2))/17)/(3+2*sqrt(2)) for n mod 15 = {1, 2, 5, 7, 11, 13}.
lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))/(((9+4*sqrt(2))/7)*((19+6*sqrt(2))/17)^2) for n mod 15 = {0, 3, 6, 12}.
lim_{n -> infinity} a(n)/a(n-1) = (3+2*sqrt(2))*((19+6*sqrt(2))/17)/((9+4*sqrt(2))/7)^3 for n mod 15 = {4, 8, 10, 14}.
lim_{n -> infinity} a(n)/a(n-1) = ((9+4*sqrt(2))/7)^4/((3+2*sqrt(2))*((19+6*sqrt(2))/17)^2) for n mod 15 = 9.

			124^2+(124+833)^2 = 15376+915849 = 931225 = 965^2.

Cf. A156835, A076296, A118120, A118554, A156035 (decimal expansion of 3+2*sqrt(2)), A156649 (decimal expansion of (9+4*sqrt(2))/7), A156163 (decimal expansion of (19+6*sqrt(2))/17).

{forstep(n=0, 50000, [3, 1], if(issquare(2*n^2+1666*n+693889), print1(n, ",")))}

a(n) = 6*a(n-15)-a(n-30)+1666 for n > 30; a(1) = 0, a(2) = 124, a(3) = 168, a(4) = 187, a(5) = 343, a(6) = 399, a(7) = 595, a(8) = 624, a(9) = 915, a(10) = 952, a(11) = 1260, a(12) = 1372, a(13) = 1768, a(14) = 1827, a(15) = 1975, a(16) = 2499, a(17) = 3135, a(18) = 3367, a(19) = 3468, a(20) = 4312, a(21) = 4620, a(22) = 5712, a(23) = 5875, a(24) = 7524, a(25) = 7735, a(26) = 9499, a(27) = 10143, a(28) = 12427, a(29) = 12768, a(30) = 13624.

G.f.: x*(124+44*x+19*x^2+156*x^3+56*x^4+196*x^5+29*x^6+291*x^7+37*x^8+308*x^9+112*x^10+396*x^11+59*x^12+148*x^13+524*x^14-108*x^15-32*x^16-13*x^17-92*x^18-28*x^19-84*x^20-11*x^21-97*x^22-11*x^23-84*x^24-28*x^25-92*x^26-13*x^27-32*x^28-108*x^29)/((1-x)*(1-6*x^15+x^30)).

Edited by Klaus Brockhaus, Feb 16 2009

A201916 Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+2737)^2 = y^2.

Original entry on oeis.org

0, 75, 203, 323, 552, 708, 1020, 1127, 1311, 1428, 1608, 1820, 1955, 2336, 2675, 3128, 3311, 3627, 3927, 4140, 4508, 4743, 5535, 6003, 6800, 7280, 7848, 8211, 8588, 9240, 9860, 11063, 11895, 13583, 14168, 15180, 15827, 16827, 18011, 18768, 20915, 22836

Offset: 1

T. D. Noe, Feb 09 2012

Note that 2737 = 7 * 17 * 23, the product of the first three distinct primes in A058529 (and A001132) and hence the smallest such number. This sequence satisfies a linear difference equation of order 55 whose 55 initial terms can be found by running the Mathematica program.
There are many sequences like this one. What determines the order of the linear difference equation? All primes p have order 7. For those p, it appears that p^2 has order 11, p^3 order 15, and p^i order 3+4*i. It appears that for semiprimes p*q (with p > q), the order is 19. What is the next term of the sequence beginning 3, 7, 19, 55, 163? This could be sequence A052919, which is 1 + 2*3^f, where f is the number of primes.
The crossref list is thought to be complete up to Feb 14 2012.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A001652 (1), A076296 (7), A118120 (17), A118337 (23), A118674 (31).
Cf. A129288 (41), A118675 (47), A118554 (49), A118673 (71), A129289 (73).
Cf. A118676 (79), A129298 (89), A129836 (97), A157119 (103), A161478 (113).
Cf. A129837 (119), A129992 (127), A129544 (137), A161482 (151).
Cf. A206426 (161), A130608 (167), A161486 (191), A185394 (193).
Cf. A129993 (199), A198294 (217), A130609 (223), A129625 (233).
Cf. A204765 (239), A129991 (241), A207058 (263), A129626 (281).
Cf. A205644 (287), A207059 (289), A129640 (313), A205672 (329).
Cf. A129999 (337), A118611 (343), A130610 (359), A207060 (401).
Cf. A129641 (409), A207061 (433), A130645 (439), A130004 (449).
Cf. A129642 (457), A129725 (521), A101152 (569), A130005 (577).
Cf. A207075 (479), A207076 (487), A207077 (497), A207078 (511).
Cf. A111258 (601), A115135 (617), A130013 (647), A130646 (727).
Cf. A122694 (761), A123654 (809), A129010 (833), A130647 (839).
Cf. A129857 (857), A130014 (881), A129974 (937), A129975 (953).
Cf. A130017 (967), A118630 (2401), A118576 (16807).

d = 2737; terms = 100; t = Select[Range[0, 55000], IntegerQ[Sqrt[#^2 + (#+d)^2]] &]; Do[AppendTo[t, t[[-1]] + 6*t[[-27]] - 6*t[[-28]] - t[[-54]] + t[[-55]]], {terms-55}]; t

a(n) = a(n-1) + 6*a(n-27) - 6*a(n-28) - a(n-54) + a(n-55), where the 55 initial terms can be computed using the Mathematica program.

G.f.: x^2*(73*x^53 +116*x^52 +100*x^51 +171*x^50 +104*x^49 +184*x^48 +57*x^47 +92*x^46 +55*x^45 +80*x^44 +88*x^43 +53*x^42 +139*x^41 +113*x^40 +139*x^39 +53*x^38 +88*x^37 +80*x^36 +55*x^35 +92*x^34 +57*x^33 +184*x^32 +104*x^31 +171*x^30 +100*x^29 +116*x^28 +73*x^27 -363*x^26 -568*x^25 -480*x^24 -797*x^23 -468*x^22 -792*x^21 -235*x^20 -368*x^19 -213*x^18 -300*x^17 -316*x^16 -183*x^15 -453*x^14 -339*x^13 -381*x^12 -135*x^11 -212*x^10 -180*x^9 -117*x^8 -184*x^7 -107*x^6 -312*x^5 -156*x^4 -229*x^3 -120*x^2 -128*x -75) / ((x -1)*(x^54 -6*x^27 +1)). - Colin Barker, May 18 2015

cp's OEIS Frontend

A118673 Positive solutions x to the equation x^2 + (x+71)^2 = y^2.

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A155923 Positive numbers y such that y^2 is of the form x^2+(x+17)^2 with integer x.

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A155464 a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 0, a(1) = 51, a(2) = 340.

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A155465 a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 7, a(1) = 88, a(2) = 555.

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A155466 a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 28, a(1) = 207, a(2) = 1248.

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A156159 Squares of the form k^2+(k+17)^2 with integer k.

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A155464 a(n) = 7a(n-1) - 7a(n-2) + a(n-3) for n > 2; a(0) = 0, a(1) = 51, a(2) = 340.

A155465 a(n) = 7a(n-1) - 7a(n-2) + a(n-3) for n > 2; a(0) = 7, a(1) = 88, a(2) = 555.

A155466 a(n) = 7a(n-1) - 7a(n-2) + a(n-3) for n > 2; a(0) = 28, a(1) = 207, a(2) = 1248.