OFFSET
1,2
COMMENTS
a(n) is odd since a(n) mod 10 = A000012(n). Since all odd numbers with one or two distinct prime factors are deficient, a(n) is deficient. E.g., 18399811 = sigma(a(3)) < 2*a(3) = 36791042. - Muniru A Asiru, Nov 17 2016
The digital root of a(n) is always 1, 4, 7 or 9. - Muniru A Asiru, Nov 29 2016
LINKS
Colin Barker, Table of n, a(n) for n = 1..380
M. A. Asiru, All square chiliagonal numbers, Int J Math Educ Sci Technol, 47:7(2016), 1123-1134.
Index entries for linear recurrences with constant coefficients, signature (1,0,80640398,-80640398,0,-1,1).
FORMULA
a(n) = 80640398*a(n-3) - a(n-6) - 40239396, for n>6.
a(n) = 40320199*a(n-3) + 1804980*A271115(n-3) - 20119698, for n>3. - Muniru A Asiru, Apr 09 2016
G.f.: x*(1+2240*x+18393280*x^2-77030438*x^3+18393280*x^4+2240*x^5+x^6) / ((1-x)*(1-80640398*x^3+x^6)). - Colin Barker, Apr 09 2016
EXAMPLE
PROG
(GAP)
g:=1000;
S:=[2*[ 500, 1 ], 4*[ 1022201, 22880 ], 498*[ 8980, 201 ], 996*[ 1, 0 ], -2*[- 500, 1 ], -4*[- 1022201, 22880 ]];; Length(S);
u:=40320199;; v:=902490;; G:=[[u, 2*(g-2)*v], [v, u]];;
A:=List([1..Length(S)], s->List(List([0..6], i->G^i*TransposedMat([S[s]])), Concatenation));; Length(A);
D1:=Union(List([1..Length(A)], k->A[k]));; Length(D1);
D2:=List(D1, i-> [(i[1]+(g-4))/(2*(g-2)), i[2]/2] );;
D3:=Filtered(D2, i->IsInt(i[1]));
D4:=Filtered(D3, i->i[2]>0);
D5:=List(D4, i->i[1]); # chiliagonal (or 1000-gonal) number is square
(PARI) Vec(x*(1+2240*x+18393280*x^2-77030438*x^3+18393280*x^4+2240*x^5+x^6)/((1-x)*(1-80640398*x^3+x^6)) + O(x^50)) \\ Colin Barker, Apr 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Muniru A Asiru, Apr 08 2016
EXTENSIONS
More terms from Colin Barker, Apr 09 2016
STATUS
approved