A274588 - OEIS

%I #12 Apr 10 2023 15:59:07

%S 1,8,638,6931,572671,6223778,514257668,5588945461,461802812941,

%T 5018866799948,414698411763098,4506936797407591,372398711960448811,

%U 4047224225205216518,334413628642071268928,3634402847297487025321,300303066121868039048281

%N Values of n such that 2*n-1 and 7*n-1 are both triangular numbers.

%H Colin Barker, <a href="/A274588/b274588.txt">Table of n, a(n) for n = 1..650</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,898,-898,-1,1).

%F Intersection of A069099 and A174114.

%F G.f.: (1+7*x-268*x^2+7*x^3+x^4) / ((1-x)*(1-30*x+x^2)*(1+30*x+x^2)).

%e 8 is in the sequence because 2*8-1 = 15, 7*8-1 = 55, and 15 and 55 are both triangular numbers.

%t CoefficientList[Series[(1 + 7 x - 268 x^2 + 7 x^3 + x^4)/((1 - x) (1 - 30 x + x^2) (1 + 30 x + x^2)), {x, 0, 16}], x] (* _Michael De Vlieger_, Jun 30 2016 *)

%t LinearRecurrence[{1,898,-898,-1,1},{1,8,638,6931,572671},20] (* _Harvey P. Dale_, Apr 10 2023 *)

%o (PARI) isok(n) = ispolygonal(2*n-1, 3) && ispolygonal(7*n-1, 3)

%o (PARI) Vec((1+7*x-268*x^2+7*x^3+x^4)/((1-x)*(1-30*x+x^2)*(1+30*x+x^2)) + O(x^20))

%Y Cf. A069099, A174114, A274587.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jun 29 2016