login
A257724
Hexagonal numbers (A000384) that are the sum of fourteen consecutive hexagonal numbers.
4
35245, 794629045, 28238642425, 640790268444865, 22771697546069605, 516734554053498696685, 18363142444517200268785, 416695777857208665553032505, 14808074793520787633419991965, 336024308655092047765242836700325, 11941261129626387046720630977591145
OFFSET
1,1
FORMULA
G.f.: -35*x*(35*x^4+8424*x^3-27932146*x^2+22702680*x+1007) / ((x-1)*(x^2-898*x+1)*(x^2+898*x+1)).
EXAMPLE
35245 is in the sequence because H(133) = 35245 = 1653 + 1770 + 1891 + 2016 + 2145 + 2278 + 2415 + 2556 + 2701 + 2850 + 3003 + 3160 + 3321 + 3486 = H(29)+...+H(42).
MATHEMATICA
LinearRecurrence[{1, 806402, -806402, -1, 1}, {35245, 794629045, 28238642425, 640790268444865, 22771697546069605}, 20] (* Harvey P. Dale, Jun 04 2017 *)
PROG
(PARI) Vec(-35*x*(35*x^4+8424*x^3-27932146*x^2+22702680*x+1007)/((x-1)*(x^2-898*x+1)*(x^2+898*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 06 2015
STATUS
approved