A268108 Even indices of Pell numbers of the form x^2 + y^2 where x, y > 0.

2, 10, 50, 58, 106, 226, 250, 290, 346, 514, 562, 842, 866, 914

Offset

1,1

Comments

Sequence focuses on the even Pell numbers.

Corresponding Pell numbers are 2, 2378, 4866752642924153522, 5616228332641321147898, 13264095873479197467931567359068050319018, ...

First differences are 8, 40, 8, 48, 120, 24, 40, ...

Links

Table of n, a(n) for n=1..14.

Example

2 is a term since A000129(2) = 2 = 1^2 + 1^2.
10 is a term since A000129(10) = 2378 = 13^2 + 47^2.
50 is a term since A000129(50) = 4866752642924153522 = 101254909^2 + 2203746829^2.

Prog

(PARI) a000129(n) = sum(k=0, n, binomial(n, 2*k+1) * 2^k);
isA000404(n) = {for(i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
for(n=1, 1e3, if(isA000404(a000129(2*n)), print1(2*n, ", ")));

Crossrefs

Cf. A000129, A000404, A001542.

Sequence in context: A279852 A219662 A355153 * A143147 A317111 A337348

Adjacent sequences: A268105 A268106 A268107 * A268109 A268110 A268111

Keyword

nonn,more

Author

Altug Alkan, Jan 26 2016

Extensions

a(9)-a(14) from Jinyuan Wang, Aug 14 2022

Status

approved