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A257723
Hexagonal numbers (A000384) that are the sum of twelve consecutive hexagonal numbers.
4
47278, 30011878, 1773905266, 1129461664906, 66759145382566, 42506160261709726, 2512413675548232778, 1599676834159716812578, 94552176198823041633886, 60202237934260622257499926, 3558376596554092673296082146, 2265651020818287423879030051706
OFFSET
1,1
FORMULA
G.f.: -2*x*(473*x^4+1620*x^3-17683432*x^2+14982300*x+23639) / ((x-1)*(x^2-194*x+1)*(x^2+194*x+1)).
EXAMPLE
47278 is in the sequence because H(154) = 47278 = 3003 + 3160 + 3321 + 3486 + 3655 + 3828 + 4005 + 4186 + 4371 + 4560 + 4753 + 4950 = H(39)+...+H(50).
MATHEMATICA
LinearRecurrence[{1, 37634, -37634, -1, 1}, {47278, 30011878, 1773905266, 1129461664906, 66759145382566}, 20] (* Harvey P. Dale, Nov 07 2017 *)
PROG
(PARI) Vec(-2*x*(473*x^4+1620*x^3-17683432*x^2+14982300*x+23639) / ((x-1)*(x^2-194*x+1)*(x^2+194*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 06 2015
STATUS
approved