OFFSET
1,1
COMMENTS
The expression 2*n^2 + c with c = 49 yields more squares than any other value of c in the range 1 < c < 100 and n < 5*10^4. - K. D. Bajpai, Nov 04 2013
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-1).
FORMULA
a(n) = 6*a(n-3) - a(n-6), with initial terms 4, 6, 14, 30, 40, 84. - T. D. Noe, Nov 04 2013
From G. C. Greubel, Aug 12 2021: (Start)
a(n) = 2*A276600(n+1).
G.f.: (2*x)*(2 + 3*x + 7*x^2 + 3*x^3 + 2*x^4)/(1 - 6*x^3 + x^6). (End)
EXAMPLE
a(12) = 2856; as 12 mod 3 = 0, a(12) = 14*A001109(12/3) = 204*14 = 2856; also 2*2856^2 = 4039^2 - 49, i.e., A106525(12)^2 - 49;
MATHEMATICA
LinearRecurrence[{0, 0, 6, 0, 0, -1}, {4, 6, 14, 30, 40, 84}, 40] (* T. D. Noe, Nov 04 2013 *)
PROG
(Magma) I:=[4, 6, 14, 30, 40, 84]; [n le 6 select I[n] else 6*Self(n-3) - Self(n-6): n in [1..41]]; // G. C. Greubel, Aug 12 2021
(Sage)
def A106526_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (2*x)*(2 +3*x +7*x^2 +3*x^3 +2*x^4)/(1 -6*x^3 +x^6) ).list()
a=A106526_list(41); a[1:] # G. C. Greubel, Aug 12 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Andras Erszegi (erszegi.andras(AT)chello.hu), May 07 2005
STATUS
approved