Lozenge tilings of hexagons with removed core and satellites

We consider regions obtained from 120 degree rotationally invariant hexagons by removing a core and three equal satellites (all equilateral triangles) so that the resulting region is both vertically symmetric invariant, give simple product formulas for number of their lozenge tilings. describe new method approach proving these formulas, full details an illustrative special case. As byproduct, we are also able to generalize this case in different direction, finding natural counterpart twenty year old formula due Ciucu, Eisenkölbl, Krattenthaler, Zare, which went unnoticed until now. The general original problem will be treated subsequent paper. then work out consequences correlation holes, were motivation study.