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A156572
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Squares of the form k^2+(k+23)^2 with integer k.
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3
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289, 529, 1369, 4225, 13225, 42025, 139129, 444889, 1423249, 4721929, 15108769, 48344209, 160402225, 513249025, 1642275625, 5448949489, 17435353849, 55789022809, 185103876169, 592288777609, 1895184495649, 6288082836025
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Square roots of k^2+(k+17)^2 are in A156567, values k are in A118337.
lim_{n -> infinity} a(n)/a(n-3) = 17+12*sqrt(2).
lim_{n -> infinity} a(n)/a(n-1) = ((627+238*sqrt(2))/23^2)^2 for n mod 3 = 1.
lim_{n -> infinity} a(n)/a(n-1) = ((27+10*sqrt(2))/23)^2 for n mod 3 = {0, 2}.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,34,-34,0,-1,1).
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FORMULA
| a(n) = 34*a(n-3)-a(n-6)-4232 for n > 6; a(1)=289, a(2)=529, a(3)=1369, a(4)=4225, a(5)=13225, a(6)=42025.
G.f.: x*(289+240*x+840*x^2-6970*x^3+840*x^4+240*x^5+289*x^6)/((1-x)*(1-34*x^3+x^6)).
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EXAMPLE
| 4225 = 65^2 is of the form k^2+(k+23)^2 with k = 33: 33^2+56^2 = 4225. Hence 4225 is in the sequence.
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PROG
| (PARI) {forstep(n=-8, 1800000, [1, 3], if(issquare(a=2*n*(n+23)+529), print1(a, ", ")))}
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CROSSREFS
| Equals A156567^2. Cf. A156575 (first trisection), A156573 (second trisection), A156574 (third trisection).
Cf. A118337, A156035 (decimal expansion of 3+2*sqrt(2)), A156164 (decimal expansion of 17+12*sqrt(2)), A156571 (decimal expansion of (27+10*sqrt(2))/23), A157472 (decimal expansion of (627+238*sqrt(2))/23^2).
Sequence in context: A184046 A008367 A152852 * A157990 A188186 A112077
Adjacent sequences: A156569 A156570 A156571 * A156573 A156574 A156575
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KEYWORD
| nonn,easy
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 11 2009
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EXTENSIONS
| Revised by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 16 2009
G.f. corrected, third comment and cross-references edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 22 2009
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