A178508 - OEIS

%I #27 Jun 30 2026 21:16:06

%S 1,7,10,13,31,49,70,97,100,130,310,490,700,970,1000,1300,3100,4900,

%T 7000,9700,10000,13000,31000,49000,70000,97000,100000,130000,310000,

%U 490000,700000,970000,1000000,1300000,3100000,4900000,7000000,9700000,10000000

%N a(n) = 1, 7, A011557*(period 6: repeat 10, 13, 31, 49, 70, 97).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,10).

%F G.f.: x*(10*x^2+13*x^3+31*x^4+49*x^5+60*x^6+27*x^7+1+7*x)/(1-10*x^6).

%F a(n) = 10^floor((n-3)/6)*(45+8*cos((n-2)*Pi)+25*cos((n-2)*Pi/3)+19*cos(2*(n-2)*Pi/3)-4*sqrt(3)*(4*sin((n-2)*Pi/3)+sin(2*(n-2)*Pi/3))) for n>2. - _Wesley Ivan Hurt_, Jun 18 2016

%p A178508:=n->10^floor((n-3)/6)*(45+8*cos((n-2)*Pi)+25*cos((n-2)*Pi/3)+19*cos(2*(n-2)*Pi/3)-4*sqrt(3)*(4*sin((n-2)*Pi/3)+sin(2*(n-2)*Pi/3))): 1,7,seq(A178508(n), n=3..50); # _Wesley Ivan Hurt_, Jun 18 2016

%t Join[{1,7},Flatten[Table[10^n {10,13,31,49,70,97},{n,0,6}]]] (* _Harvey P. Dale_, Nov 19 2013 *)

%t (* Alternative: *)

%t Join[{1,7},LinearRecurrence[{0,0,0,0,0,10},{10,13,31,49,70,97},50]] (* _Harvey P. Dale_, Nov 19 2013 *)

%o (PARI) a=[1,7,10,13,31,49,70,97];for(i=1,99,a=concat(a,10*a[#a-5])); a \\ _Charles R Greathouse IV_, Jun 01 2011

%Y Cf. A007770, A000012, A171250.

%K nonn,easy

%O 1,2

%A _Paul Curtz_, May 29 2010

%E Dissassociated with sums-of-squares sequences by _R. J. Mathar_, Jun 07 2010