A257723 Hexagonal numbers (A000384) that are the sum of twelve consecutive hexagonal numbers.

47278, 30011878, 1773905266, 1129461664906, 66759145382566, 42506160261709726, 2512413675548232778, 1599676834159716812578, 94552176198823041633886, 60202237934260622257499926, 3558376596554092673296082146, 2265651020818287423879030051706

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..435

Index entries for linear recurrences with constant coefficients, signature (1,37634,-37634,-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

Cf. A257721, A257722, A257724.

Sequence in context: A254479 A227710 A215840 * A320621 A218097 A293584

Adjacent sequences: A257720 A257721 A257722 * A257724 A257725 A257726

Keyword

nonn,easy

Author

Colin Barker, May 06 2015

Status

approved